Question

3, Gosha is a smart fellow. He gets an A in a course 80% of the time. Still, he likes his leisure, only studying for the final exam in half of his courses. Nevertheless, when he does study, he is almost sure (95% likely) to get an A. Assuming he got an A, how likely is it that he studied? If someone estimates the above to be 75%, what error are they committing? Explain.

Answer 1

Solution to Part-a

Since he studies in only half of his courses so:

P(Studied) = 0.5

Probability of him getting An A, P(A) = 0.8

P(Studied | A) = P(A | Studied) * P(Studied)/P(A)

P(Studied | A) = 0.95 * 0.5/0.8 = 0.59375 Ans.

Solution to Part-b

Since chances of Gosha studying is 50%, then someone would have guessed it to be around that base rate.

Here they have committed the "Base rate neglect" error. They have downplayed the base rate(which is 0.5 in this case), and have put too much weight into sample data(which is him getting an A, probability of which is 0.8).So that have estimated it to be .75, which is wrong.