Question

the mathematics department of a college has 10 male professors, 8 female professors, 9 male teaching assistants, and 14 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female.
the probability is (type an integer or a fraction. simplify your answer)

Explanation:

Step1: Calculate total number of people

$10 + 8+9 + 14=41$

Step2: Calculate number of teaching - assistants

$9 + 14=23$

Step3: Calculate number of females

$8 + 14=22$

Step4: Calculate number of female teaching - assistants

$14$

Step5: Use the formula for the probability of the union of two events $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

The number of people who are teaching - assistants or females is $23+22 - 14=31$

Step6: Calculate the probability

The probability $P=\frac{31}{41}$

Answer:

$\frac{31}{41}$