Question

A physics class has 50 students. Of​ these, 10 students are physics majors and 17 students are female. Of the physics​ majors, three are female. Find the probability that a randomly selected student is female or a physics major.

PLEASE ROUND TO THREE DECIMAL PLACES

Answer 1

We are assuming that the randomly selected student is a female or a physics major or both.

Total students = 50

P(Female) = P(F) = 17/50

P(Physics major) = P(M) = 10/50

P( Physics major | Female) = P(M | F) = 3/50

So, it's asking you for the union of Female and Physics major. The formula for union is

P ( M U F ) = P(M) + P(F) - P(M | F) = 10/50 + 17/50 - 3/50 = 0.480

You can think of this as adding all the female and physics major and then subtracting all of the female physics major since they are counted twice.