If the student is found to have earned an A grade, find the probability that he or she is a senior, that is P(D|A).

Question

A class of introductory probability consists of 20 sophomores, 30 juniors and 50 seniors. The final grades show that 4 sophomores, 6 juniors and 10 senior received an A grade. Randomly choose a student from the class. Assume B, C and D are the events that the student is a sophomore, junior and senior student, respectively. Let A be the event that the student got an A grade.

(a) If the student is found to have earned an A grade, find the probability that he or she is a senior, that is P(D|A).

(b) Find P(C) and P(C|A).

(c) Are “getting an A grade” and “being a junior” independent events? How about the events of “getting an A grade” and “being a senior”?

Answer 1

(a) P(D|A) = P(D∩A) / P(A) = (10/100) / (20/100) = 0.5

(b) P(C) = 30/100 = 0.3

P(C|A) = P(C∩A) / P(A) = (6/100) / (20/100) = 0.3

(c) The events "getting an A grade" and "being a junior" are independent, since P(C|A) = P(C). Similarly, the events "getting an A grade" and "being a senior" are independent, since P(D|A) = P(D).

Hope this helps!