At a certain university, 30% of the students major in math. Of the students majoring in math, 60% are males. Of all the students at the university, 70% are males.
a) What is the probability that a student selected at random in the university is male and majors in math?

b) What is the probability that a randomly selected student in the university is female or majors in math or both?

Based upon the information you provided, out of every 100 students you have this breakdown:
male, math major: 18
female, math major: 12
male, non-math major: 52
female, non-math major: 18

a) 18%
b) female: 30%
math major (either sex): 30%
female math major: 12%

so for b), you just add them up to get 72%?

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  1. this probably wrong, see correct answer below
    P(Math) = 0.30
    P(Male | Math) = 0.60
    P(Male) = 0.70

    P(Male ∩ Math) = P(Male | Math) ⋅ P(Math) = 0.60 ⋅ 0.30 = 0.18

    P(Female) = P(¬Male) = 1 − P(Male) = 1 − 0.70 = 0.30
    P(Math) = 0.30
    P(Female | Math) = P(¬Male | Math) = 1 − P(Male | Math) = 1 − 0.60 = 0.40
    P(Female ∩ Math) = P(Math) ⋅ P(Female | Math) = 0.30 ⋅ 0.40 = 0.12

    P(Female ∪ Math) = P(Female) + P(Math) − P(Female ∩ Math) = 0.30 + 0.30 − 0.12 = 0.48

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