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?
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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 $nq(1-q)=$ $__________$.