Question: Suppose the conditional probability that a student received a grade A for English, given that the student is female, is 0.15. For simplicity, let us

Suppose the conditional probability that a student received a grade A for English, given that the student is female, is 0.15. For simplicity, let us also assume the school has a total of 1,000 students, among which 60% are female.

(1) What is the conditional probability that a student did not receive a grade A, given that the student is female?

(2) Can we calculate the conditional probability that a student received a grade A for English, given that the student is male?

(3) Suppose now we know the conditional probabilities of male and female students getting A are 0.10 and 0.15, respectively. How do we use the conditional probabilities to calculate the “unconditional” probability that a student (whether male or female) received a grade A for English?

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