# Flip another coin each time, whats the mean times required?

Start with one coin, flip all coins, if all land on tails then stop, otherwise add another coin and repeat.

What is the mean average number of flips?

This is not a homework question.

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$$\prod_{k=1}^\infty\left(1-2^{-k}\right)\approx0.288788\;$$
@alan2here: this chance is very small, $2^{-k}$ whenever you have $k$ coins. Just as an example, would this chance be not that small, say $\frac1k$, then the infinite product $\prod_k (1-\frac1k) =0$, but it's not the case. –  Ilya Jan 11 '13 at 14:26
@alan2here: If you're finding it difficult to get an intuition for infinite products $\prod_ka_k$, note that you can rewrite them as $\exp\left(\sum_k\log a_k\right)$, and presumably you're familiar with the fact that $\sum_k\log a_k$ need not diverge to negative infinity. –  joriki Jan 11 '13 at 16:20