Suppose that n independent tosses of a coin having probability p of coming up heads are made. Show that the probability that an even number of heads results is (1/2)(1+(q-p)^n) where q=1-p. Do this by utilizing the identity
sigma from i=0 to n/2 of (n choose 2i) p^2i q^(n-2i)=(1/2)[(p=q)^n+(q-p)^n]
where n/2 is the largest integer less than or equal to n/2.
I tried expanding it, but every time i end up with p^n only.
Thanks so much!!