Coin Flip

[tubbyspencer]

If I flip a coin one hundred times, what's the chance it comes up heads exactly 50 times?

What about a thousand flips(that it comes up heads exactly 500 times)?

(And, if you don't mind, show me how to calculate that as well... thanks)

[aces961]

[ QUOTE ]
If I flip a coin one hundred times, what's the chance it comes up heads exactly 50 times?

What about a thousand flips(that it comes up heads exactly 500 times)?

(And, if you don't mind, show me how to calculate that as well... thanks)

[/ QUOTE ]

For the case of 100 flips and 50 heads. (.5^50)*(.5^50)*(100 choose 50)

n choose r is (n factorial)/((r factorial)(n-r factorial))

You can generalize this for 500 and 1000 just replace the numbers as needed.

The equation is calculating the probability that the first 50 tosses are heads and the next 50 are tails, then the 100 choose 50 mulitplies that by the number of ways to arrange those tosses.

[pzhon]

Stirling's formula is a good approximation: n! ~ SquareRoot(2 pi n) (n/e)^n.

By Stirling's formula, if you toss a fair coin 2n times, the probability of exactly n heads is roughly 1/SquareRoot(pi n). For n=500, the exact answer is 0.025225... = 1/39.643. This approximation gives 0.025231... = 1/39.633.

[lorinda]

Handy Binomial Calculator. (http://faculty.vassar.edu/lowry/binomialX.html)

Lori