Question

43% of the all students are first generation students, 28% are minority students, and 17% are both first generation and minority. What is the probability that a randomly selected student a) is exactly in one of these categories (only first generation or only minority)? b) is not in any of these categories? c) is a first generation student but not a minority?

Answer 1

Ans:

Let

A=first generation

B=minority

P(A)=0.43

P(B)=0.28

P(A and B)=0.17

P(A or B)=P(A)+P(B)-P(A and B)

=0.43+0.28-0.17

=0.54

a)

P(only A or only B)=P(A or B)-P(A and B)

=0.54-0.17=0.37

b)

P(neither A nor B)=1-P(A or B)

=1-0.54=0.46

c)

P(A but not B)=P(A)-P(A and B)

=0.43-0.17=0.26