Shots to make five baskets

Question

A player makes each shot independently with probability 0.6. She shoots until she has made 5 baskets in total. On average, how many shots does that take?

Accepted Answer

Making 5 baskets is five independent single-make waits stacked one after another. Each make has probability p = 0.6 and expected wait 1/p, so for r = 5 makes, E = \frac{r}{p} = \frac{5}{0.6} = \frac{25}{3} \approx 8.33 	ext{ shots.} Takeaway. Expected shots to the r-th make is r/p; here 5/0.6 = 25/3 \approx 8.33.

Shots to make five baskets

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