Question

A class consists of 60% men and 40% women. Blonde men compose 25% of the class, and blond women make up 20% of the class. If a student is chosen at random and is found to be a male, what is the probability that the student is blond?

Answer 1

The probability that the student is blond and chosen be men is 65%.

Explanation:

Given : A class consists of 60% men and 40% women. Blonde men compose 25% of the class, and blond women make up 20% of the class. If a student is chosen at random and is found to be a male.

To find : What is the probability that the student is blond?

Solution :

Let the probability of men is 60% P(M)=0.6

The probability of women is 40% P(W)=0.4

Let B is the person blonde makeup.

The probability of blonde men is 25% P(B/M)=0.25

The probability of blonde women is 20% P(B/W)=0.20

We have to find the probability that the student is blonde and choosen is men i.e. P(M/B)

Applying Baye's Theorem,

`P(M/B)=(P(B/M)* P(M))/(P(B/M)* P(M)+P(B/W)* P(W))`

`P(M/B)=(0.25* 0.6)/(0.25* 0.6+0.20* 0.4)`

`P(M/B)=(0.15)/(0.15+0.08)`

`P(M/B)=(0.15)/(0.23)`

`P(M/B)=0.65`

Therefore, The probability that the student is blond and chosen be men is 65%.

Answer 2

The probability that a selected male student is blond = 25/60 = 5/12 = 0.42