Question

at a certain non-profit organization, 40% of employees are college graduates and 35% of employees have more than ten years of experience. if 1% of the organizations 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)?

write your answer as a decimal (not as a percentage). (if necessary, consult a list of formulas.)

Explanation:

Define the events and given probabilities

Using the Probability of Events knowledge point, we define:

• Let \(G\) be the event that a randomly selected employee is a college graduate.
• Let \(E\) be the event that a randomly selected employee has more than ten years of experience.

From the problem statement, we have:

• \(P(G) = 40\% = 0.40\)
• \(P(E) = 35\% = 0.35\)
• \(P(G \cap E) = 11\% = 0.11\)

Apply the addition rule of probability

Using the Addition Rule of Probability knowledge point, we find the probability that a randomly selected employee is either a college graduate or has more than ten years of experience (or both):

$$ P(G \cup E) = P(G) + P(E) - P(G \cap E) $$

Substituting the given values:

$$ P(G \cup E) = 0.40 + 0.35 - 0.11 $$

Calculate the final probability

We perform the arithmetic:

$$ P(G \cup E) = 0.75 - 0.11 = 0.64 $$

Answer:

At a certain non-profit organization, 40% of employees are college graduates and 35% of employees have more than ten years of experience. If 11% 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)?

Write your answer as a decimal (not as a percentage). (If necessary, consult a list of formulas.) <blank>0.64</blank>