Chapter 13.6, Problem 22PPS

To determine

To determine the probability.

Answer to Problem 22PPS

Probability is $0.904$ or 90.4%

Explanation of Solution

Given information :

Total are 50.

31% among them recycle

Total = 50

31% recycles

69% do not recycle

We have to determine the probability that if two people are selected than exactly one of them must recycle.

Probability that none of them recycles $=\frac{69}{100}\cdot \frac{69}{100}$

Probability that first, between the two recycles $=\frac{31}{100}\cdot \frac{69}{100}$

Probability that second, between them recycles $=\frac{69}{100}\cdot \frac{31}{100}$

Therefore probability that at most one of them recycles is,

P(at most one of two recycles) = $=\frac{69}{100}\cdot \frac{69}{100}+\frac{31}{100}\cdot \frac{69}{100}+\frac{69}{100}\cdot \frac{31}{100}=\frac{9039}{10000}$ or 90.4%