Business Degree Certification Practice Test

What is the probability that both positions of sales manager and sales associate are filled by men, assuming equal chances among three men and three women?

1. 0.20

2. 0.25

3. 0.33

4. 0.50

The correct answer is: 0.20

To determine the probability that both the sales manager and the sales associate positions are filled by men, we first need to analyze the total combination of possible outcomes. In this scenario, there are three men and three women, making a total of six candidates. The positions of sales manager and sales associate can be filled in succession. Therefore, we can calculate the probability step by step: 1. When filling the position of the sales manager, the probability of selecting a man first is 3 out of 6, since there are three men. 2. Once the sales manager, who is a man, is chosen, there are now only five candidates left—two men and three women. The probability of then selecting a man for the sales associate position is 2 out of the remaining 5 candidates. To calculate the combined probability of both events (choosing a man for sales manager followed by choosing a man for sales associate), we multiply the probabilities: - The probability of selecting a man for the sales manager is 3/6. - The probability of selecting a man for sales associate afterward is 2/5. Thus, the overall probability can be calculated as follows: \[ \text{Probability} = \left(\frac{3}{6