Question

In a class of 87 people, 27 wear glasses, 32 are blonde, and 38 are neither blonde nor wear glasses. Find the probability that a student chosen at random will have blonde hair and wear glasses?

Answer 1

Total 87 people in class.

Let , Event A : People in class who wear glasses

#( A ) = Number of people in class who wear glasses = 27

Event B : people in class who have blonde hair = 32

#( B ) = Number of people in class who have blonde hair = 32

#( A or B )^c : Number of people who neither blonde nor wear glasses = 38

So,

#( A or B ) : Number of people who have blond hair or wear glasses = 87 - 38 = 49

Number of people who have both blond hair and wear glasses is ,

#( A and B ) = #( A ) + #(B) - #( A or B ) = 27+32- 49 = 10

General formula of probability is ,

Probability = Number of favorable outcomes / Total outcomes.

We have to find probability that a student chosen at random will have blonde hair and wear glasses

In notation we have to find P( A and B )

P( A and B ) = #( A and B ) / 87

P( A and B ) = 10/87

P( A and B ) = 0.11494

Probability that a student chosen at random will have blonde hair and wear glasses is 0.11494