Question

At a certain non-profit organization, 65% of employees are college graduates and of employees have more than ten years of experience. If of the organization's employees both have more than ten years of experience and are college graduates, what is the probability that a randomly selected employee will be either a college graduate or have more than ten years of experience (or both)

Answer 1

The probability is 27%.

Explanation:

We are not given the percentage value for the employees, so we choose an assumed percentage value of 35%

Also; Let assume that if 73% of the organization's employees both have more than ten years of experience and are college graduates ....

Using the Set theory:

Let represent the college graduates to be group A; &

Let represent the experienced employees to be group B.

A = 65% of the population

B = 35% of the population; &

A U B (union of A and B) = 73%.

The objective here is to determine the probability that a randomly selected employee will be either a college graduate or have more than ten years of experience (or both)

i.e We need to determine the size of A ∩ B ; which is read as : (intersection of A and B )

(i.e the group of college grads with 10 yrs experience).

Thus;

P( A U B) = P(A) + P(B) - P(A ∩ B )

P(A ∩ B) = P(A) + P(B) - P(A U B)

P(A ∩ B) = 0.65 + 0.35 - 0.73 = 0.27

Thus ,the probability is 27%.