Question

An exam is graded by one of two teaching assistants, chosen with equal likelihood (by flipping a fair coin_. The first teaching assistant ("Alice") gives every exam an A; the second teaching assistant ("Bob") gives every exams a randomly chosen letter grade (A,B,C,D,F) all with equal likelihood.

If a student's exam is graded as an A, what is the probability that it was graded by teaching assistant Alice?

Answer 1

We are given here that: P(Alice) = P(Bob) = 0.5

Also, we are given that: P(A | Alice) = 1 and

P(A | Bob) = P(B | Bob) = P(C | Bob) = P(D | Bob) = P(F | Bob) = 1/5 = 0.2

Using law of total probability, we get here:

P(A) = P(A | Bob)P(Bob) + P(A | Alice)P(Alice) = 0.2*0.5 + 1*0.5 = 0.6

Using bayes theorem, we get here:

P(Alice | A) = P(A | Alice)P(Alice) / P(A) = 1*0.5 / 0.6 = 5/6

Therefore 5/6 is the required probability here.