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50% or a million/2 because of the fact the probability is: h and h h and t t and h t and t and because in basic terms 2 are the two heads and tails 2/4 is 50%. besides the shown fact that, if its the risk of having heads and then one tails in that order may well be 25% because of the fact in basic terms one answer may well be interior the the.


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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.
Join them; it only takes a minute: I'm working on heads and tails game probability maths exercise and came across this question.
The second throw is unnecessary.
The result is TT; The outcome: {H, TH, TT}.
In probability problems, you need to be careful about choosing your sample space.
You can only assume that events will all be equally likely if they're all qualitatively the same and there's nothing other than names and labels please click for source distinguish them from each other.
The prototypical examples are the two sides of a coin and the six sides of a six-sided die.
In your case, on the other hand, the event H is qualitatively different from the two events TH and TT, so there's no reason to expect that these three will be equiprobable, and the principle of indifference doesn't apply.
To apply it, you need to look at qualitatively similar events.
In this case, that would be HH, HT, TH and TT.
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What others are saying Probability Activities MEGA Pack of Math Worksheets and Probability Games This is a fun table top activity or addition to the math center to allow students the chance to see what is likely, more likely, and equal in chance.


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Now let's start to do some more interesting problems.
And one of these things that you'll find in probability is that you can always do a more interesting problem.
So now I'm going to think about-- I'm going to take a fair coin, and I'm going to flip it three times.
And I want to find the probability of at least one head out of the three flips.
So the easiest way to think about this is how many equally likely possibilities there are.
In the last video, we saw if we flip a coin 3 times, there's 8 possibilities.
For the first flip, there's 2 possibilities.
Second flip, there's 2 possibilities.
and the beast game download lagu in the third flip, there are 2 possibilities.
So 2 times 2 times 2-- there are 8 equally likely possibilities if I'm flipping a coin 3 times.
Now how many of those possibilities have at least 1 head?
Well, we drew all the possibilities over here.
So we just have to count how many of these have at least 1 head.
So that's 1, 2, 3, 4, 5, 6, 7.
So 7 of these have at least 1 head in them.
And this last one does not.
So 7 of the 8 have at least 1 head.
Now you're probably thinking, OK, Sal.
You were able to do it by writing out all of the possibilities.
But that would be really hard if I said at least one head out of 20 flips.
This had worked well because I only had 3 flips.
Let me make it clear, this is in 3 flips.
This would have been a lot harder to do or more time consuming to do if I had 20 flips.
Is there some shortcut here?
Is there some other way to think about it?
And you couldn't just do it in some simple way.
You can't just say, oh, the probability of heads times the probability of heads, because if you got heads the first time, then now you don't the game kiss and tell to get heads anymore.
Or you could get heads again-- you don't have to.
So it becomes a little bit more complicated.
But there is an easy way to think about it where you could use this methodology right over here.
You'll actually see this on a lot of exams where they make it seem like a harder problem, but if you just think about in the right way, lakers and bulls tickets of a sudden it becomes simpler.
One way to think about it is the probability of at least 1 head in 3 flips is the same thing-- this is the same thing-- as the probability of not getting all tails, right?
If we got all tails, then we don't have at least 1 head.
So these two things are equivalent.
The probability of getting at least 1 head in 3 flips is the same thing as the probability of not getting all tails in 3 flips.
So what's the probability of not getting all tails?
Well, that's going to be 1 minus the probability of getting all heads and tails game probability />The probability of getting all tails, since it's 3 flips, it's the probability of tails, tails, and tails.
Because any of the other situations are going to have at least 1 head in them.
And that's all of the other possibilities, and then this is the only other leftover possibility.
If you add them together, you're going to get 1.
Let me write it heroes game and generals modes way.
Let me write it a new color just so you see where this is coming from.
The probability of not all tails plus the probability of all tails-- well, this is essentially exhaustive.
This is all of the possible circumstances.
So your chances of getting either not all tails or all tails-- and these are mutually exclusive, so heads and tails game probability can add heads and tails game probability />The probability of not all tails or, just to be clear what we're doing, the probability of not all tails or the probability of all tails is going to be equal to one.
These are mutually exclusive.
You're either going to have not all tails, which means a head shows up.
Or you're going to have all tails.
But you can't have both of these things happening.
And since they're mutually exclusive and you're saying the probability of this or this happening, you could add their probabilities.
And this is essentially all of the possible events.
So this is essentially, if you combine these, this is the probability of any of the events happening.
And that's going to be a 1 or 100% chance.
So another way to think about is the probability of not all tails is going to be 1 minus the probability of all tails.
So that's what we did right over here.
And the probability of all tails is pretty straightforward.
So this is going to be 1 minus the probability of getting all tails.
So we can apply that to a problem that is harder to do than writing all of the scenarios like we did in the first problem.
Let's say we have 10 flips, the probability of at least one head in 10 flips-- well, we use the same idea.
This is going to be equal to the probability of not all tails in 10 flips.
So we're just saying the probability of not getting all of the flips going to be tail.
All heads and tails game probability the flips is tails-- not all tails in 10 flips.
And this is going to be 1 minus the probability of flipping tails 10 times.
So it's 1 minus 10 tails in a row.
And so this is going to be equal to this part heads and tails game probability over here.
Let me write this.
So this is going to be this one.
Let me just rewrite it.
This is equal to 1 minus-- and this part is going to be, well, one tail, another tail.
And I'm going to do this 10 times.
Let me write this a little neater.
And so we really just have to-- the numerator is going to be 1.
So this is going to be 1.
This is going to be equal to 1.
This is going to be equal to 1 minus-- our numerator, you just have 1 times itself 10 times.
And then on the denominator, you have 2 times 2 is 4.
This is the exact same thing as 1 is 1024 over 1024 minus 1 over 1024, which is equal to 1,023 over 1,024.
We have a common denominator here.
So 1,000-- I'm doing that same blue-- over 1,024.
So if you flip a coin 10 times in a row-- a fair coin-- you're probability of getting at least 1 heads in that 10 flips is pretty high.
It's 1,023 over 1,024.
And you can get a calculator out to figure that out in terms of a percentage.
Actually, let me just do that just for fun.
So if we have 1,023 divided by 1,024 that gives us-- you have a 99.
So this is if we round.
This is equal to 99.
And I rounded a little bit.
It's actually slightly, even slightly, higher than that.
And this is heads and tails game probability pretty powerful tool or a pretty powerful way to think about it because it would have taken you forever to write all of the scenarios down.
In fact, there would have been 1,024 scenarios to write down.
So doing this exercise for 10 flips would have taken up all of our time.
But when you think about in a slightly different way, when you just say, look the probability of getting at least 1 heads in 10 flips is the same thing as the probably of not getting all tails.
And that's 1 minus the probability of getting all tails.
And this is actually a pretty easy thing to think about.

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The coin can only land on one side or the other (event) but there are two possible outcomes: heads or tails. One over two is a half, or 50 per cent. What's not so obvious is that the probability of a coin that has come up heads for the past 19 flips also landing heads up on the 20th throw is also 50 per cent.


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Probability: Tossing 2 Coins (Head/Tail)

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Explore the probability of a one-coin toss using the Heads and Tails Game. This is an easy game for young learners. All you need to play is the Heads and Tails gameboard, two coins for markers and another coin to flip. Use a coin toss to decide who will be heads and who will be tails. Then the fun begins!


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What is the best strategy to win the game in the fewest number of steps possible? Obviously 2 of the coins will either be heads or tails. So that is important to take into account. However, I don't know which ones are heads/tails. I keep turning this into a probability problem but don't seem to be getting anywhere. Any help?


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Expected Coin Flips for k Heads in a Row

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Online virtual coin toss simulation app. Simulate a random coin flip or coin toss to make those hard 50/50 decisions from your mobile Android, iPhone, or Blackberry phone or desktop web browser.


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If you're seeing this message, it means we're having trouble loading external resources on our website.
Now let's start to do some more interesting problems.
And one of these things that you'll find in probability is that you can always do a more interesting problem.
So now I'm going to think about-- I'm going to take a fair coin, and I'm going to flip it three times.
And I want to find the probability of at least one head out of the three flips.
So the easiest way to think about this is how many equally likely possibilities there are.
In the last video, we saw if we flip a game snake and online career ladder 3 times, there's 8 possibilities.
For the first flip, there's 2 possibilities.
Second flip, there's 2 possibilities.
And in the third flip, there are 2 possibilities.
So 2 times 2 times 2-- there are 8 equally likely possibilities if I'm flipping a coin 3 times.
Now how many of those possibilities have at least 1 head?
Well, we drew all the possibilities over here.
So we just have to count how many of these have at least 1 head.
So that's 1, 2, 3, 4, 5, 6, 7.
So 7 of these have at least 1 head in them.
And this last one does not.
So 7 of the 8 have at least 1 head.
Now you're probably thinking, OK, Sal.
You were able to do it by writing out all of the possibilities.
But that would be really hard if I said at least one head out of 20 flips.
This had worked well because I only had 3 flips.
Let me make it clear, this is in 3 flips.
This would have been a lot harder to do or more time consuming to do if I had 20 flips.
Is there some shortcut here?
Is there some other way to think about it?
And learn more here couldn't just do it in some simple way.
You can't just say, oh, the probability of heads times the probability of heads, because if you got heads the first time, then now you don't have to get heads anymore.
Or you could get heads again-- you don't have to.
So it becomes a little bit more complicated.
But there is an easy way to think about it where you could use this methodology right heads and tails game probability here.
You'll actually see this on a lot of exams where they make it seem like a harder problem, but if you just think about in the right way, all of a sudden it becomes simpler.
One way to think about it is the probability of at least 1 head in 3 flips is the same thing-- this is the same thing-- as the probability of heads and tails game probability getting all tails, right?
If we got all tails, then we don't have at least 1 head.
So these two things are equivalent.
The probability of getting at least 1 head in 3 flips is the same thing as the probability of not getting all tails in 3 flips.
So what's the probability of not getting all tails?
Well, that's going to be 1 minus the probability of getting all tails.
The probability of getting all tails, since it's 3 flips, it's the game cops and robbers of tails, tails, and tails.
Because any of the other situations are going to have at least 1 head in them.
And that's all of the other possibilities, and then this is the only other leftover possibility.
If you add them together, you're going to get 1.
Let me write it this way.
Let me write it a new color just so you see where this is coming from.
The probability of not all tails plus the probability of all tails-- well, this is essentially exhaustive.
This is all of the possible circumstances.
So your chances of getting source heads and tails game probability all tails or all tails-- and these are mutually exclusive, so we can add them.
The probability of not all tails or, just to be clear what we're doing, the probability of not all tails or the probability of all tails is going to be equal to one.
These are mutually exclusive.
You're either going to have not all tails, which means a head shows up.
Or you're going to have all tails.
But you can't have both of these things happening.
And since they're mutually exclusive and you're saying the probability of this or this happening, you could add their probabilities.
And this is essentially all of the possible events.
So this is essentially, if you combine these, this is the probability of any of the events happening.
And that's going to be a 1 or 100% chance.
So another way to think about is the probability of not all tails is going to be 1 minus the probability of all tails.
So that's what we did right over here.
And the probability of all tails is pretty straightforward.
So this is going to be 1 minus the probability of getting all tails.
So we can apply that to a problem that is harder to do than writing all of the scenarios like we did in the first problem.
Let's say we have 10 flips, the probability of at least one head in 10 flips-- well, we use the same idea.
This is going to be equal to the probability of not all tails in 10 flips.
So we're just saying the probability of not getting all of the flips going to be tail.
All of the flips is tails-- not all tails in 10 flips.
And this is going to be 1 minus the probability of flipping tails 10 times.
So it's 1 minus 10 tails in a row.
And so this is going to be equal to this part right over here.
Let me write this.
So this is going to be this one.
Let me just rewrite it.
This is equal to 1 minus-- and this part is going to be, well, one tail, another tail.
And I'm going to do this 10 times.
Let me write this a little neater.
And so we really just have to-- the numerator is going to be 1.
So this is going to click the following article 1.
This is going to be equal to 1.
Let me do it in that same color of green.
This is going to be equal to 1 minus-- our numerator, you just have 1 times itself 10 times.
And then on the denominator, you have 2 times 2 is 4.
This is the exact same thing as 1 is 1024 over 1024 minus 1 over 1024, which is equal to 1,023 over 1,024.
We have a common denominator here.
So 1,000-- I'm doing that same blue-- over 1,024.
So if you flip a coin 10 times in a row-- a fair coin-- you're probability of getting at least 1 heads in that 10 flips is pretty high.
It's 1,023 over 1,024.
And you can get a calculator out to figure that out in terms of a percentage.
Actually, let me just do that just for fun.
So if we have 1,023 divided by 1,024 that gives us-- you have a 99.
So this is if we round.
This is equal to 99.
And I rounded a little bit.
It's actually slightly, even slightly, higher than that.
And this is a pretty powerful tool or a pretty powerful way to think about it because it would have taken you forever to write all of the scenarios down.
In fact, there would have been 1,024 scenarios to write down.
So doing this exercise for 10 flips would have taken up all of our time.
But when you think about in a slightly different way, when you just say, look the probability of getting at least 1 heads in 10 flips is heads and tails game probability same thing as the probably of not getting all tails.
And that's 1 minus the probability of getting all tails.
And this is actually a pretty easy thing to think about.

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The most famous of these is the Law of Large Numbers, which mathematicians, engineers, economists, and many others use every day.In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails.


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Join them; it only takes a minute: I'm working on a maths exercise and came across this question.
The second throw is unnecessary.
The result is TT; The outcome: {H, TH, TT}.
In probability problems, you need to be careful about choosing your sample space.
You can only assume that events will all be article source likely if they're all qualitatively the same and there's nothing other than names and labels to distinguish them from each other.
The prototypical examples are the two sides of a coin and the six sides of a six-sided die.
In your case, on the other hand, the event H is qualitatively different from the two events TH and TT, so there's no reason to expect that these three will be equiprobable, and the principle of indifference doesn't apply.
To apply it, you need to look at qualitatively similar events.
In this case, that would be HH, Heads and tails game probability, TH and TT.
Thanks for contributing an answer to Mathematics Stack Exchange!
Provide details and share your research!
Use MathJax to format equations.
To learn more, see our.
Browse other questions tagged or.

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Demonstrate flipping a coin and calling heads or tails before the coin lands. Play a quick game of Heads or Tails before explaining probability and how partners can play the game. Ask all of the children to stand in a circle around you as you flip the coin.


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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.
Join them; it only takes a minute: I'm working on a maths exercise and came across this question.
The second throw is heads and tails game probability />The result is TT; The outcome: {H, TH, TT}.
In probability problems, you need to be careful about choosing your sample space.
You can only assume that events will all be equally likely if they're all qualitatively the same and there's nothing other than names and labels to distinguish them from each other.
The prototypical examples are the two sides of a coin and the six sides of a six-sided die.
In your case, on the other hand, the event H is qualitatively different from the two events TH and TT, so there's no reason to expect that these three will be equiprobable, and the principle of indifference doesn't apply.
To apply it, you need to look at qualitatively similar events.
In this case, that would be HH, HT, TH and TT.
Thanks for heads and tails game probability an answer to Mathematics Stack Exchange!
Provide details and share your research!
Use MathJax to format equations.
To learn more, see our.
Browse other questions tagged or.

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Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to choose between two alternatives, sometimes used to resolve a dispute between two parties.


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If you're seeing this message, it means we're having trouble loading external resources on our website.
Now let's start to do some more interesting problems.
And one of these things that you'll find in probability is that you can always do a more interesting problem.
So now I'm going to think about-- I'm going to take a fair coin, and I'm going to flip it three times.
And I want to find the probability of at least one head out of the three flips.
So the easiest way to think about click is how many equally likely possibilities there are.
In the last video, we saw if we flip a coin 3 times, there's 8 possibilities.
For the first flip, there's 2 possibilities.
Second flip, there's 2 possibilities.
And in the third flip, there are 2 possibilities.
So 2 times 2 times 2-- there are 8 equally likely possibilities if I'm flipping a coin 3 times.
Now how many of those possibilities have at least 1 head?
Well, we drew all the possibilities over here.
So we just have to count how many of these have at least 1 head.
So that's 1, 2, 3, 4, 5, 6, 7.
So 7 of these have at least 1 head in them.
And this last one does not.
So 7 of the 8 have at least 1 head.
Now you're probably thinking, OK, Sal.
You were able to do heads and tails game probability by writing out all of the possibilities.
But that would be really hard if I said at least one head out of 20 flips.
This had worked well because I only had 3 flips.
Let me make it clear, this is in 3 flips.
This would have been a lot harder to do or more time consuming to do if I had 20 flips.
Is there some shortcut here?
Is there some other way to think about it?
And you couldn't just do it in some simple way.
You can't just say, oh, the probability of heads times the probability of heads, because if you got heads the first time, then now you don't have to get heads anymore.
Or you could get heads again-- you don't have to.
So it becomes a little bit more complicated.
But there is an easy way to think about it where you could use this methodology right over here.
You'll actually see this on a lot of exams where they make it seem like a harder problem, but if you just think about in the right way, all of a sudden it becomes simpler.
If we got all tails, then we don't have at least 1 head.
So these two things are equivalent.
The probability of getting drawing and guessing game least 1 head in 3 flips is the same thing as the probability of not getting all tails in 3 flips.
So what's the heads and tails game probability of not getting all tails?
Well, that's going to be 1 minus the probability of getting all tails.
The probability of getting all tails, since it's 3 flips, it's the probability of tails, tails, and tails.
Because any of the other situations are going to have at least 1 head in them.
And that's all heads and tails game probability the other possibilities, and then this is the only other leftover possibility.
If you add them together, you're going to get 1.
Let me write it this way.
Let me write it a new color just so you see where this heads and tails game probability coming from.
The probability of not all tails plus the probability of all tails-- well, this is essentially exhaustive.
This is all of the possible circumstances.
So your chances of getting either not all tails or all tails-- and these are mutually exclusive, so we can add them.
The probability of not all tails or, just to be clear what we're doing, the probability of not all tails or the probability of all tails is going to be equal to one.
These are mutually exclusive.
You're either going to have not all tails, which means a head shows up.
Or you're going to have all tails.
But you can't have both of these things happening.
And since they're mutually exclusive and you're saying the probability of this or this happening, you could add their probabilities.
And this is essentially all of the possible events.
So this is essentially, if you combine these, this is the probability of any of the events happening.
And that's going to be a 1 or 100% chance.
So another way to think about is the probability of not all tails is going to be 1 minus the probability of all tails.
So that's what we did right over here.
And the probability of all tails is pretty straightforward.
So this is going to be 1 minus the probability of getting all tails.
So we can learn more here that to a problem that is harder to do than writing all of the scenarios like we did in the first problem.
Let's say we have 10 flips, the probability of at least one head in 10 flips-- well, we use the same idea.
This is going to be equal to the probability of not all tails in 10 flips.
So we're just saying the probability of not getting all of the flips going to be tail.
All of the flips is tails-- not all tails in 10 flips.
And this is going to be 1 minus the probability of flipping tails 10 times.
So it's 1 minus 10 tails in a row.
And so this is going to be equal to this part right over here.
Let me write this.
So this is going to be this one.
free games no download and for me just rewrite it.
This is equal to 1 minus-- and this part is going to be, well, one tail, another tail.
And I'm going to do this 10 times.
Let me write this a little neater.
And so we really just have to-- the numerator is going to be 1.
So this is going to be 1.
This is going to be equal to 1.
Let me do it in that same color of green.
This is going to be equal to 1 minus-- our numerator, you just have 1 times itself 10 times.
And then on the denominator, you have 2 times 2 is 4.
This is the exact same thing as 1 is 1024 over 1024 minus 1 over 1024, which is equal to 1,023 over 1,024.
We have a common denominator here.
So 1,000-- I'm doing that same blue-- over 1,024.
So if you flip a coin 10 times in a row-- a fair coin-- you're probability of getting at least 1 heads in that 10 flips is pretty high.
It's 1,023 over 1,024.
And you can get a calculator out to figure that out in terms of a percentage.
Actually, let me just do that just and ratios interactive games fun.
So if we have 1,023 divided by 1,024 that gives us-- you have a 99.
So this is if we round.
This is equal to 99.
And I rounded a little bit.
It's actually slightly, even slightly, higher than that.
And this is a pretty powerful tool or a pretty powerful way to think about it because it would have taken you forever to write all of the scenarios down.
In fact, there would have been 1,024 scenarios to write down.
So doing this exercise for 10 flips would have taken up all of our time.
But when you think about in a slightly different way, when you just say, look the probability of getting at least 1 heads in 10 flips is the same thing as the probably of not getting all tails.
And that's 1 minus the probability of getting all tails.
And this is actually a pretty easy thing to think about.

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Why not try a quick game of Heads or Tails. It is a simple fundraising idea, easy to manage and all guests can participate. All you need is a two-sided coin, an energetic presenter, a willing audience and a prize for the winner. Heads or Tails is a perfect revenue boost for events where your audience is seated. However, it can be adapted to fit.


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statistics - Heads or tails probability - Mathematics Stack Exchange
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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.
Join them; it only takes a minute: I'm working on a maths exercise and came across this question.
The second throw is unnecessary.
The result is TT; The outcome: {H, TH, TT}.
In probability problems, you need to be careful about choosing your sample space.
You can only assume that events will all be equally likely if they're all qualitatively the same and there's nothing other than names and labels to distinguish them from each other.
The prototypical examples are the two sides of a coin and the six sides of a six-sided die.
In your case, on the heads and tails game probability hand, the event H is qualitatively different from the two events TH and TT, so there's no reason to expect that these three will be equiprobable, and the principle of indifference doesn't apply.
To apply it, you need to look at qualitatively similar events.
In this case, that would be HH, Https://entermarket.ru/and-games/snake-and-career-ladder-online-game.html, TH and TT.
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could model the process that causes heads or tails to occur, but this would not be necessary for just about anything we’re going to need. Instead, if we assume that the coin is fair, we can model the event β€œheads” as occurring with probability 1/2, and the event β€œtails” as occurring with the same probability.


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If you're seeing this message, it means we're having trouble loading external resources on our website.
Now let's start to do some more https://entermarket.ru/and-games/estimating-and-rounding-online-games.html problems.
And one of these no download games free for and that you'll find in probability is that you can always do a more interesting problem.
So now I'm going to think about-- I'm going to take a fair coin, and I'm going to flip it three times.
And I want to find the probability of at least one head out of the three flips.
So the easiest way to think about this is how many equally likely possibilities there are.
In the last video, we saw if we flip a coin 3 times, there's 8 possibilities.
For the first flip, there's 2 possibilities.
Second flip, there's 2 possibilities.
And heads and tails game probability the third flip, there are 2 possibilities.
So 2 times 2 times 2-- there are 8 equally likely possibilities if I'm flipping a coin 3 times.
Now how many of those possibilities have at least 1 head?
Well, we drew all the possibilities over here.
So we just have to count how many of these have at least 1 head.
So that's 1, 2, 3, 4, 5, 6, 7.
So 7 of these heads and tails game probability at least 1 head in them.
And this last one does not.
So 7 of the 8 have at least 1 head.
Now you're probably thinking, OK, Sal.
You were able to do it by writing out all of the possibilities.
But that would be really hard if I said at least st day games activities head out of 20 flips.
This had worked well heads and tails game probability I only had 3 flips.
Let me make it clear, this is in 3 flips.
This would have been a lot harder to do or more time consuming to https://entermarket.ru/and-games/games-batman-and-superman.html if I had 20 flips.
Is there some shortcut here?
Is there heads and tails game probability other way to think about it?
And you couldn't just do it in some simple way.
You can't just say, oh, the source of heads times the probability of heads, because if you got heads the first time, then now you don't have to get heads anymore.
Or you could get heads again-- you don't have to.
So it becomes a little bit more complicated.
But there is an easy way to think about it where you could use this methodology right heads and tails game probability here.
You'll actually see this on a lot of exams where they make more info seem like a harder problem, but if you just think about in the right way, all of a sudden it becomes simpler.
One way to think about it is the probability of at least 1 head in 3 flips is the same thing-- this is the same thing-- as the probability of not getting all tails, right?
If we got all tails, then we don't have at least 1 head.
So these two things are equivalent.
The probability of getting at least 1 head in 3 flips is the same thing as the probability of not getting all tails in 3 flips.
So what's the probability of not getting all tails?
Well, that's going to be 1 minus the probability of getting all tails.
The probability of getting all tails, since it's 3 flips, it's the probability of tails, tails, and tails.
Because any of the other situations are going to have at least 1 head in them.
And that's all of the other possibilities, and then this is the only other leftover possibility.
If you add them together, you're going to get 1.
Let me write it this way.
Let me write it a new color just heads and tails game probability you see where this is coming from.
The probability of not all tails plus the probability of all tails-- well, this is essentially exhaustive.
This is all of the possible circumstances.
So your chances of getting either not all tails or all tails-- and these are mutually exclusive, so we can add them.
The probability of not all tails or, just to be clear what we're doing, the probability of not all tails or the probability of all tails is going to be equal to one.
These are mutually exclusive.
You're either going to have not all tails, which means a head shows up.
Or you're going to have all tails.
But you can't have both of these things happening.
And since they're mutually exclusive and you're saying the probability of this or this happening, you could add their probabilities.
And this is essentially all of the possible events.
So this is essentially, if you combine these, this is the probability of any of the events happening.
So another way to think about is the probability of not all tails is going to be 1 minus the heads and tails game probability of all tails.
So that's what we did right over here.
And the probability of all tails is pretty straightforward.
So this is going to be 1 minus the probability of getting all tails.
So we can apply that to a problem that is harder to do than writing all of the scenarios like we did in the first problem.
Let's say we have 10 flips, the probability of at least one head in 10 flips-- well, we use the same idea.
This is going to be equal to the probability of not all tails in 10 flips.
So we're just saying the probability of not getting all of the flips going to be tail.
All of the flips is tails-- not all tails in 10 flips.
And this is going to be 1 minus the probability of flipping tails 10 times.
So it's 1 minus 10 tails in a row.
And so this is going to be equal to this part right over here.
Let me write this.
So this is going to be this one.
Let me just rewrite it.
This is equal to 1 minus-- and this part is going to be, well, one tail, another tail.
And I'm going to do this 10 times.
Let me write this a little neater.
And so we really just have to-- the numerator is going to be 1.
So this is going to be 1.
This is going to be equal to 1.
Let me do it in that same color of green.
This is going to be equal to 1 minus-- our numerator, you just have 1 times itself 10 times.
And then on the denominator, you have 2 times 2 is 4.
This is the exact same thing as 1 is 1024 over 1024 minus 1 over 1024, which is equal to 1,023 over 1,024.
We have a common denominator here.
So 1,000-- I'm doing that same blue-- over 1,024.
So if you flip a coin 10 times in a row-- a fair coin-- you're probability of getting at least 1 heads in that 10 flips is pretty high.
It's 1,023 over 1,024.
And you can get a calculator out to figure that out in terms of a percentage.
Actually, let me just do that just for fun.
So if we have 1,023 divided by 1,024 that gives us-- you have a 99.
So this is if we round.
This is equal to 99.
And I rounded a little bit.
It's actually slightly, even slightly, higher than that.
And this is a pretty powerful tool or a pretty powerful way to think about it because it would have taken you forever to write all of the scenarios down.
In fact, there would have been 1,024 scenarios to write down.
So doing this exercise for 10 flips would have taken up all of our time.
But when you think about in a slightly different way, when you just say, look the probability of getting at least 1 heads in 10 flips is the same thing as the probably of not getting all tails.
And that's 1 minus the probability of getting all tails.
And this is actually a pretty easy thing to think about.

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New study shows how guessing heads or tails isn't really a 50-50 game. By Daily Mail Reporter.. Diaconis determined that the probability of guessing which side comes up of a spinning penny is.


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Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to choose between two alternatives, sometimes used to resolve a dispute between two parties.


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Unfortunately, it's an β€œit depends” answer. In every day life, the probability of getting heads or tails is extremely close to 1. The reason for this has to do with the normal definition of a β€œflip”, which is a rotation of the coin along the x or.


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Probability Distribution Table - Intro with tossing a coin 3 times

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Students explore probability by flipping a penny. Go Premium. Get unlimited, ad-free access to all of TeacherVision's printables and resources for as low as $2.49 per month.


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Counter-Intuitive Probability. Coin Flips To HH Versus HT Are Not The Same!