If a basketball player is a 90% free-throw shooter what are the chances he makes 106 in a row?
Chances a 90% free throw shooter makes 106 straight baskets?
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0That would roughly be an expected value for the number of shots you'd need to make. Of course it would be no guarantee. And an honest calculation would be very difficult, since each of the trials of 106 consecutive shots will not be independent. (A failure of perfect shots 1 through 106 likely means a failure of shots 2 through 107 as well.) – 2012-10-30
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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%.