Question

Sixty percent of a firm's employees are men. Suppose four of the firm's employees are randomly selected. a. What is more likely, finding three men and one woman or two men and two women? Finding three men and one woman is more likely. The probabilities of finding three men and one woman, and two men and two women are the same. Finding two men and two women is more likely. ︵ b. Do you obtain the same answer as in part a if 70% of the firm's employees had been men? No, finding three men and one woman is more likely. Yes, the probabilities of finding three men and one woman, and two men and two women are the same. No, Finding two men and two women is more likely. Yes, finding three men and one woman is more likely.

Answer 1

Calculating the probabilities using the binomial distribution formula reveals which scenario of selecting employees is more likely. The higher the percentage of male employees, the higher the probability of selecting more men from the workforce.

Step-by-step explanation:

To determine what is more likely, finding three men and one woman or two men and two women, we need to calculate the probabilities for each case. Assuming 60% of the firm's employees are men, the probability of selecting three men and one woman can be calculated using the binomial distribution formula: P(X=3) = C(4,3) * (0.6)^3 * (0.4)^1. On the other hand, the probability of selecting two men and two women is: P(X=2) = C(4,2) * (0.6)^2 * (0.4)^2. After calculating these probabilities, we can compare them to see which scenario is more likely.

If 70% of the firm's employees were men, the calculation would be similar but with different probabilities reflecting the new percentage of male employees. The same binomial distribution formula would be used, just replacing the probability of selecting a man with 0.70 and a woman with 0.30 in each case. Therefore, as the percentage of male employees increases, the probability of selecting three men also increases, making it more likely to pick three men and one woman.