Question

A physics class has 40 students. Of​ these, 17 students are physics majors and 13 students are female. Of the physics​ majors, five five are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is

Answer 1

General rule for two events:

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

A ==> Student is a Physics major

B ==? Student is a female

Probability = Number of favorable outcome / number of possible outcome

17 of the 40 students are physics major

P (A) = 17/40

13 of the 40 students are female

P (B) = 13/40

5 of the 40 students are physics major and female

P (A and B) = 5/40

So use the general rule :

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

= (17 + 13 + 5) / 40

=35/40

=0.875

The probability that a randomly selected student is female or a physics major is 0.875