Archie is taking a course in probability theory. Discussion sessions with the cl

Question

Archie is taking a course in probability theory. Discussion sessions with the class TA (teaching assistant) conflict with Archie's trips to the beach. Archie has to decide between attending TA sessions, which might help him do better in the probability course, and going to the beach. Archie learns that % of past students who did not attend TA sessions received a grade of B or below in the course. Archie also learns that % of past students received a grade higher than B. After some thought, Archie decides to attend the TA sessions. Not all of his classmates share his decision; in fact, only out of every of his classmates attend discussion sessions with the TA. Compute the probability that Archie will receive a grade higher than a B in the course. Round your answer to two decimal places.

Explanation / Answer

Let T be the event that the student attends TA sessions.
Let B be the event that the student earns higher than a B.

We are given P(B) = 0.15, P(T) = 10/13, and P(not B|not T) = 0.95
We need to find P(B|T), which by definition is P(B and T)/P(T).
We already know P(T) = 10/13, but we still need to find P(B and T) first.

Note that 0.95 = P(not B|not T)
= P(not B and not T) / P(not T)
= P(not B and not T) / (1 - P(T))
= P(not B and not T) / 3/13

and so P(not B and not T) = 0.95(3/13) = 0.2192
Therefore, P(B or T) = 1 - P(not B and not T) = 1 - 0.2192 = 0.7808

Since P(B or T) = P(B) + P(T) - P(B and T),
P(B and T) = P(B) + P(T) - P(B or T) = 0.15 + 10/13 - 0.7808 = 0.1384

Now we can finish the problem. Archie's probability of getting higher than a B is
P(B|T) = P(B and T)/P(T) = 0.1384/(10/13) = 0.18 or 18%

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