Question

Use Bayes's Theorem to calculate the probability prompted for in the following scenario. Indicate your answer...

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)?

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