In a large organization,55% of all employees are female,25% of the employees have a business degree,and 40% of all males have a business degree.What is the probability that one randomly selected employee will be either a female or have a business degree?
A)0.29
B)0.41
C)0.67
D)0.73
E)0.83

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the probability of the union of two events, which is: P(A or B) = P(A) + P(B) - P(A and B)

Let A be the event that the employee selected is female, and let B be the event that the employee selected has a business degree. Then, we can calculate:

P(A) = 0.55 (given in the problem)
P(B) = 0.25 (given in the problem)
P(A and B) = P(B | male) * P(male) = 0.4 * 0.45 = 0.18  (using the conditional probability formula and the fact that 45% of the employees are male)

Therefore, we can plug these values into the formula above to get:

P(A or B) = P(A) + P(B) - P(A and B) = 0.55 + 0.25 - 0.18 = 0.62

So the probability that one randomly selected employee will be either a female or have a business degree is 0.62, which corresponds to choice D.

In a Large Organization,55% of All Employees Are Female,25% of the Employees