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**

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