# Thread: even and odd probability of coin

1. ## even and odd probability of coin

hi,
i am preparing for an exam and i wondered if some one could show me explicitly
how to calculate the probability of getting an even number of heads in flipping a coin, with probability p for heads n times.
i know i need to sum a series but i can't manage to do it well.
something that doesn't use too advanced math.

2. p=probability for heads,
n=number of throws....

the probability of getting an even number of heads can be expressed
by expanding the binomial,
or logically as follows....

even number of heads={no heads and n tails} or {2 heads and n-2 tails} or {4 heads and n-4 tails} or {6 heads and n-6 tails} or.......etc
and we must count all the ways these pairings can occur.

the probability is P(0H and nT)+P(2H and [n-2]T)+........

$\displaystyle =(1-p)^n+\binom{n}{2}p^2(1-p)^{n-2}+\binom{n}{4}p^4(1-p)^{n-4}+......$