Suppose that 60% of the students do homework regularly. It is also known that 80% of students who had been doing homework regularly end up doing well in the course. Only 20% of students who had not been doing homework regularly end up doing well in the course. What is the probability that a student does well in the course?
A) 0.080
B) 0.480
C) 0.560
D) 0.857

Question

Quizplus · Accepted Answer

To find the probability that a student does well in the course, we can use the law of total probability. Let's denote:- $P(H)$ as the probability of doing homework regularly, which is 0.60.- $P(\neg H)$ as the probability of not doing homework regularly, which is 1 - 0.60 = 0.40.- $P(W|H)$ as the probability of doing well given that a student does homework regularly, which is 0.80.- $P(W|\neg H)$ as the probability of doing well given that a student does not do homework regularly, which is 0.20.The probability that a student does well in the course, $P(W)$, can be calculated as:$$P(W) = P(W|H)P(H) + P(W|\neg H)P(\neg H)$$$$P(W) = (0.80)(0.60) + (0.20)(0.40)$$$$P(W) = 0.48 + 0.08$$$$P(W) = 0.56$$Therefore, the probability that a student does well in the course is 0.56.

Suppose That 60% of the Students Do Homework Regularly