Employment data at a software company reveal that 41% of employees have a computer science degree,36% are women and half of the women have a computer science degree.What is the probability that a randomly chosen employee is female or has a computer science degree?
A)0.77
B)0.23
C)0.18
D)0.41
E)0.59

Question

Quizplus · Accepted Answer

We can use the formula for the probability of the union (or) of two events:

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

where A and B are the events "female employee" and "employee with a computer science degree", respectively.

P(A) = 0.36 (from the employment data)
P(B) = 0.41 (from the employment data)
P(A and B) = P(B|A) * P(A) = 0.5 * 0.36 = 0.18 (since half of the women have a computer science degree, and the probability of selecting a woman is already accounted for in P(A))

Plugging these values into the formula, we get:

P("female or computer science degree") = 0.36 + 0.41 - 0.18 = 0.59

Therefore, the probability that a randomly chosen employee is female or has a computer science degree is 0.59, which corresponds to choice (E).

Employment Data at a Software Company Reveal That 41% of Employees