Final answer:
The correct option is b) 0.25. The probability that both the sales manager and sales associate positions will be filled by men is 0.25, or 1 in 4. This is calculated by multiplying the probability of selecting a man first (3/6) by the probability of selecting a man second (2/5).
Step-by-step explanation:
The question is asking about the probability that both positions of sales manager and sales associate will be filled by men, given an equal chance of selection among three men and three women. To calculate this, we need to consider the process of selecting two people for the positions without replacement.
First, the probability of selecting a man for the position of sales manager is 3/6, as there are three men out of six applicants. Once a man is selected for the first position, there are now five applicants left, two of which are men. Therefore, the probability of selecting another man for the second position of sales associate is 2/5.
To find the overall probability of both positions being filled by men, we multiply the individual probabilities:
P(both men) = P(first man) × P(second man) = \(\frac{3}{6}\) × \(\frac{2}{5}\) = \(\frac{1}{2}\) × \(\frac{2}{5}\) = \(\frac{1}{5}\).
The correct option is b) 0.25.