Question

Use Bayes's Theorem to calculate the probability prompted for in the following scenario. Indicate your answer as a percentage. Type your numeric answer into the space provided.

Your cousin Jeffrey studies for final exams 75 percent of the time. When Jeffrey studies for a final exam, he receives a grade of B or higher 80 percent of the time. When Jeffrey does not study for a final exam, he receives a grade of B or higher only 60 percent of the time.

Apply Bayes's Theorem to the scenario just described. If Jeffrey receives a grade of B or higher on his next final exam, what is the probability that he studied for the exam (expressed as a percentage)?

Answer 1

Let E shows the event that Jeffrey studies for final exams. And G shows the event that he receives a grade of B or higher.

From given information we have

P(E ) = 0.75, P(E') = 1- P(E) = 1 - 0.75 = 0.25

P(G | E) = 0.80, P(G |E' ) = 0.60

Now by the Bayes's Theorem,  the probability that he studied for the exam (expressed as a percentage) is

P(E | G) = [ P(G|E)P(E) ] / [ P(G|E)P(E) + P(G|E')P(E') ] = [ 0.80 * 0.75] / [ 0.80 * 0.75 + 0.60 * 0.25] = 0.60 / 0.75 = 0.80

Answer: 80%