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

Make a table

A grade

yes no total

sophomore 4 16 20

junior 6 24 30

senior 10 40 50

20 80 100

probability student getting an A is a senior = 10/20 = 1/2

probability a junior = 30/100 = 3/10

probability student getting an A is a junior = 6/20 = 3/10

probability getting an A grade = 20/100 = 1/5

probability being a junior = 3/10

probability getting an A grade and being a junior = 6/100 = 3/50

1/5 * 3/10 = 3/50, so independent

probability of being a senior = 1/2

probability of getting an A grade and being a senior = 1/5 * 1/2 = 1/10

probability of getting a A grade and being a senior = 1/10

so independent