Flips until the first head

Question

You flip a fair coin repeatedly until it lands heads, then stop. On average, how many flips does it take to get your first head?

Accepted Answer

Each flip is heads with probability 	frac12, independently. The number of flips until the first head follows a geometric distribution, whose average is one over the success probability: E[	ext{flips until first head}] = \frac{1}{1/2} = 2. The intuition: heads happens about half the time, so on average you need two flips to see one. You can also reason directly: your first flip always occurs; half the time it is heads and you stop, half the time you start over needing the same expected number E again. That gives E = 1 + 	frac12 E, so E = 2. Takeaway. Expected tries to the first success is \…

Flips until the first head

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