# Chances a 90% free throw shooter makes 106 straight baskets?

If a basketball player is a 90% free-throw shooter what are the chances he makes 106 in a row?

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What are your own ideas on how to approach the question? – Dilip Sarwate Oct 13 '12 at 2:19
If all the free throws are independent of one another, this is a binomial process. Since you're asking for the conjunction of events, 0.9^k is the probability of making k straight shots, so 0.9^106=0.0000141158 is the probability of making 106. Probability&statistics 101. – alancalvitti Oct 13 '12 at 2:32
@PatrickLi wasn't aware that was part of the process – jim_shook Oct 13 '12 at 5:37
Of course the assumption that successive shots are independent is unrealistic. But that never stopped homework writers. – GEdgar Oct 13 '12 at 18:33
@Gedgar True. Though this one wasn't a homework question (someone added that tag), I did it once when practicing and consider myself a 90% shooter :) – jim_shook Oct 28 '12 at 22:48

## 1 Answer

Given that the shooter makes 90% of its shots, the odds it makes $n$ shots in a row is given by the formula $p = 0.9^n$. Therefore, the odds of it making 106 shots in a row is simply $0.9^{106}$, which equals roughly 0.000014, or 0.0014%.

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