Answer to Question #258098 in Statistics and Probability for thuỳ đỗ

Question

yamaha is giving away a free motorbike to one of their 155 best customers. In this group, 55 are women, 70 are married and 40 are married men. The marital status can be only married or single.

(a) what is the probability that the motorbike will be awarded to someone who is single?

(b) given the winner is married, what is the probability that it is a woman?

Answer 1

There are 155 customers: 55 women and 100 men.

70 of them are married: 30 married women and 40 married men.

85 of them are single: 25 single women and 60 single men.

(a) Let C = the winner is single. Then $P(C)=\frac{85}{155}=\frac{17}{31}$

(b) Let A = the winner is a woman, B = the winner is married.

$P(A|B)=\frac{P(A\cap B)}{P(B)}$ = the probability that the winner is a woman, if it is given that the winner is married.

A$\ \cap$ B = the winner is a married woman.

$P(A\cap B)=\frac{30}{155}$ and $P(B)=\frac{70}{155}$

$P(A|B)=\frac{30/155}{70/155}=\frac{30}{70}=\frac{3}{7}$

Answer: (a) $\frac{17}{31}$ (b) $\frac{3}{7}$ .