To determine the probability that a randomly selected management trainee is a male who did not attend college, we need to follow these steps:
1. Identify the probability that the trainee is male:
[tex]\( P(\text{male}) \)[/tex]
2. Identify the conditional probability that a male did not attend college, which can be expressed as:
[tex]\( P(\text{did not attend college} \mid \text{male}) \)[/tex]
The overall probability can be calculated by multiplying these two probabilities together, represented as:
[tex]\[ P(\text{male}) \times P(\text{did not attend college} \mid \text{male}) \][/tex]
So, the correct notation is:
[tex]\[ P(\text{male}) \times P(\text{did not attend college} \mid \text{male}) \][/tex]
Therefore, the correct choice is:
[tex]\[ P(\text{male}) \times P(\text{did not attend college} \mid \text{male}) \][/tex]
Explanation of Probabilities:
- [tex]\( P(\text{male}) = 0.20 \)[/tex] (since 20% of the trainees are male)
- [tex]\( P(\text{did not attend college} \mid \text{male}) = 1 - P(\text{attended college} \mid \text{male}) = 1 - 0.78 = 0.22 \)[/tex]
Hence,
[tex]\[ P(\text{male}) \times P(\text{did not attend college} \mid \text{male}) = 0.20 \times 0.22 = 0.044 \][/tex]
This means there is approximately a 4.4% chance that a randomly selected management trainee is a male who did not attend college.
