# A coin has probability p of landing heads.

A coin has probability p of landing heads. 100 such coins are flipped and afterwards, every coin that landed tails is flipped again. What is the variance of the number of heads?

-
Got something from the answer below? –  Did Feb 9 '13 at 10:02
the distribution is binomial, and the variance is $nq(1-q)= n(2p-p^2)(1-2p+p^2)$ –  user59036 Feb 10 '13 at 20:05

Hint: Each coin has the same probability $q$ to show heads at the end of the procedure, independently of the others. This may happen either because it first showed heads, or because it first showed tails, was flipped again, and then showed heads. Hence $q=$ $________$. There are $n=100$ coins. Thus the distribution of the number of heads is $____________$, whose variance is $nq(1-q)=$ $__________$.
Read: probability q to show heads at the end of the procedure. –  Did Feb 7 '13 at 18:37