In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did not attend college?
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A. B. C. D. E.Explanation
Prob. of choosing a female=0.8. Prob. of a female not attending college = 0.1. So 0.8*0.1 = 0.08.
To solve this problem, we need to use conditional probability. Let's break down the information given:
We are interested in finding the probability of selecting a female trainee who did not attend college. Let's denote the event "F" as selecting a female trainee and the event "C" as selecting a trainee who attended college.
We want to find P(F and not C), which represents the probability of selecting a female trainee who did not attend college.
To solve this, we can use the following formula:
P(F and not C) = P(F) * P(not C | F)
The probability of selecting a female trainee is given as 0.8, and the probability of not attending college given that the trainee is female can be calculated as:
P(not C | F) = 1 - P(C | F)
The probability of attending college given that the trainee is female can be calculated as:
P(C | F) = (P(C and F)) / P(F)
We have the probability of selecting a female trainee who attended college as 0.9, and the probability of selecting a female trainee is 0.8.
P(C and F) = P(F) * P(C | F) = 0.8 * 0.9 = 0.72
Now, we can calculate P(not C | F) using the formula:
P(not C | F) = 1 - P(C | F) = 1 - (P(C and F) / P(F)) = 1 - (0.72 / 0.8) = 1 - 0.9 = 0.1
Finally, we can calculate P(F and not C) using the formula mentioned earlier:
P(F and not C) = P(F) * P(not C | F) = 0.8 * 0.1 = 0.08
Therefore, the probability that the person selected is a female who did not attend college is 0.08. So, the correct answer is D.