Question

At a certain non-profit organization, 51% of employees are college graduates and 47% of employees have more than ten years of experience. If 77% of the organization's employees are either college graduates or have more than ten years of experience (or both), what is the probability that a randomly selected employee will have more than ten years of experience and be a college graduate?

Answer 1

Answer: 0.21

Explanation:

Let A denotes the event that employees are college graduates.

B denotes that the event that employees have more than ten years of experience.

As per given , we have

P(A)=0.51

P(B)=0.47

P(A∪B)=0.77

We know that ,
`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

`0.77=0.51+0.47-P(A\cap B)`

`P(A\cap B)=0.51+0.47-0.77=0.21`

Hence, the probability that a randomly selected employee will have more than ten years of experience and be a college graduate = 0.21