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

Let \(C\) 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 are given:

• The probability of selecting a college graduate is \(P(C) = 40\% = 0.40\).
• The probability of selecting an employee with more than ten years of experience is \(P(E) = 35\% = 0.35\).
• The probability that an employee is both a college graduate and has more than ten years of experience is \(P(C \cap E) = 11\% = 0.11\).

We apply the concept of Probability of Events to represent these percentages as decimal values.

Apply the addition rule of probability

We want to find the probability that a randomly selected employee is either a college graduate or has more than ten years of experience (or both). This is represented by the union of the two events, \(P(C \cup E)\).

Using the Addition Rule of Probability, we have:

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

Calculate the final probability

Substitute the given decimal values into the formula:

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

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

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).

<blank>0.64</blank>