Question

In an NCAA basketball game, a certain player was identified as being an 80% free throw shooter; that is, when executing that scoring opportunity, the player would convert it into points 80% of the time. If we consider each free throw as an independent outcome,

(a) what is the probability that 5 free throw opportunities would be required to see the first one converted into points?

(b) what is the expected number of free throws required to see one converted into points?

Answer 1

Clearly its Geometric  distribution .

pmf of Geometric distribution is given by

, x= 0,1,2,3,.... , 0<p<1,q=1-p, k > or = 0

here x = 5

and also probability of throw shooter is 0.80 i.e p = 0.80

i.e q=1-0.80 = 0.20

And the expected number of free throws required to see one converted into points