Probability of K People Tossing Coins n Times

[nbalderaz]

K people independently toss a coin n times. What is the probability that all K of them get the same number of heads?
(1) Find a formula for the probability in terms of K and n.
(2) Evaluate the probability for K = {5, 10, 20} and n = {4, 8, 16}

 

[Aphex_Twin]

Let me see if I remember this:


P(n)=C(n,x)*pi^x*(1-pi)^(n-x)

Where P(n) is the probability that an x number of events will occur out of n number of tries. pi is the certainty (in the case of a coin with 2 sides pi=1/2). C(n,x) is: n!/((n-x)!*k!)

Apply the formula K-1 times.