Answer to Question #152477 in Statistics and Probability for Yosef

Question

A sports marketer randomly selects persons on the street until he encounters someone who attended a game last season. What is the probability the market encounters x = 3 people who did not attend a game before the first success when p = 0.20 of the = population attended a game?

X- Geometric(3,0.20)

Answer 1

Here we have:

p = 0.2

X = 3

q = 1 – p = 1 – 0.2 = 0.8

X follows geometric distribution

The probability that the sport marketer encounters 3 people before he finds the one who attended a game last season:

$P(X=3)=pq^{x-1}=0.2\cdot0.8^{3-1}=0.2\cdot0.8^2=0.128$

There is 12.8% chance that the sport marketer would have to select 3 people before he would find one who attended the last season game.