Question

A certain basketball player makes 80% of his free throws. Assume that results of successive free throws are independent of each other. At the end of a particular practice session the coach tells the player to begin shooting free throws and stop immediately after the first unsuccessful shot. What is the probability that the player will throw the ball at most four times?

Answer 1

Solution:

        We are given that: probability of successful shot = 80% = 0.80 then probability of unsuccessful shot = 1 - 0.80 = 0.20 and results of successive free throws are independent of each other.

        At the end of a particular practice session the coach tells the player to begin shooting free throws and stop immediately after the first unsuccessful shot.

Thus let X = Number of successful shot before first unsuccessful shot follows Geometric distribution with

p = probability of unsuccessful shot = 0.20

Thus q = 1 - p = 1 - 0.20 = 0.80

Probability mass function of geometric distribution is:
   ,   x = 0 , 1 , 2 , 3 ,........

We have to find : the probability that the player will throw the ball at most four times .

That is: we have to find: