In a recent season, hockey player Evgeni Malkin scored 50 goals in 75 games he played. Assume that his goal production stayed at that level for the next season. Find the probability that he would get his first goal (a) in the first game of the season, (b) in the second game of the season, and (c) within the first three games of the season.

Solution:

Step 1 of 4:

Given that, a hockey player Evgeni Malkin scored 50 goals in 75 games he played.

Here,

= 0.67

q = 1 - p

= 1- 0.67

= 0.33

The corresponding distribution is a Geometric distribution. Because we want to know the probability of the first person who has the characteristic.

The pmf of a Geometric distribution is

for k = 1,2,3,….