A professor has noticed that even though attendance is not a component of the gr

Question

A professor has noticed that even though attendance is not a component of the grade for his class, students who attend regularly obtain better grades. In fact, 40% of those who attend regularly receive As in the class, while only 10% of those who do not attend regularly receive As. About 70% of students attend class regularly. Find the following percentages: The percentage who receive As given that they attend class regularly. The percentage who receive As given that they do not attend class regularly. The overall percentage who receive As.

Explanation / Answer

Let

R = regularly attending
A = gets an A

a)

P(A|R) = 40% [ANSWER, given]

b)

P(A|R') = 10% [ANSWER, given]

**********

c)

By Bayes' Rule,

P(A) = P(R) P(A|R) + P(R') P(A|R')

= 0.70*0.40 + (1-0.70)*0.10

= 0.31 [ANSWER]

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