How would i figure this out? (probability of coin flips)

[LogicX]

So on a different forum I go to someone said something about flipping a coin 1 million times, and that the probability of it landing on heads 800,000 times is small, but possible. I want to come of with some mindblowing way of telling them that no, it is not realistically possible.

So what is the probability of that happening, and had you started flipping when the universe began, 1 flip a second, would you likely have achieved that result yet (6.5 billion years= 2.05x10^17 seconds)? I'm guessing not, but it would interesting to figure out.

I haven't done any probability since high school so I'm kind of clueless.

 

[HallsofIvy]

The probability of getting 800,000 heads in 1,000,000 flips of a fair coin is
$$\frac{1000000!}{80000!20000! (2^{100000})}$$

 

[disregardthat]

Are you talking about exactly 800,000 or at least 800,000?

 

[LogicX]

At least I guess.

 

[kmwest]

Probability of 800000+ heads is:


((1/2)^1000000)* [sigma ((1000000!/(800000+n)!(200000-n)!))]

sum for n=0 to 200000, this will sum all probabilities from 8000000 to 1000000 heads.

 

[statdad]

At least I guess.

For numbers of this magnitude the best way to do the probability calculation would be to use the normal approximation.

 

[dav2008]

For numbers of this magnitude the best way to do the probability calculation would be to use the normal approximation.

To follow up on this: http://www.regentsprep.org/Regents/math/algtrig/ATS7/BLesson3.htm

 

[moonman239]

Worth noting... the closer the probability of an event that has a binomial or Poisson distribution gets to 50%, the closer the normal distribution comes to the binomial distribution. Since the probability of heads in a coin toss is 50%, that means that heads are normally distributed.

 

[HallsofIvy]

So on a different forum I go to someone said something about flipping a coin 1 million times, and that the probability of it landing on heads 800,000 times is small, but possible. I want to come of with some mindblowing way of telling them that no, it is not realistically possible.

Well, one thing you will have to do is explain what you mean by "realistically possible". Even if something has a probability of 0.000000000001, it is certainly possible that it will occur on the first trial.

So what is the probability of that happening, and had you started flipping when the universe began, 1 flip a second, would you likely have achieved that result yet (6.5 billion years= 2.05x10^17 seconds)? I'm guessing not, but it would interesting to figure out.

I haven't done any probability since high school so I'm kind of clueless.