Question

The NBA season free throw record holder is Jose Calderon who made 151 of 154 (98.05%) free throws in his 2008-2009 season with the Toronto Raptors. If his free throws during the season can be considered independent, what is the minimum number of free throws he would be required to take in order for you to be at least 80% certain that he will miss one or more free throws?

Answer 1

here, probability of making = 0.9805

probability of missing .p=1-0.9805 = 0.0195

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let n be number of goals required

X be free throws miss

so, P(X≥1)=0.8

1-P(X<1) = 0.8

P(X<1) = 0.2

P(X=0) = 0.2

nC0*0.0195^0*0.9805^n = 0.2

0.9805^n = 0.2

taking natural log both side

n =ln0.2/ln0.9805 = 81.727

so, minimum number of free throws required = 82