Question

Giving a test to a group of students, the grades and gender are summarized below

A    B C Total

Male 8    9 2 19

Female 10 13 20 43

Total 18 22 22 62

If one student is chosen at random,

1. Find the probability that the student got a C:

2. Find the probability that the student was male AND got a "B":

3. Find the probability that the student was male OR got an "B":

4. If one student is chosen at random, find the probability that the student got a 'C' GIVEN they are male:

Answer 1

a) P(C) = 22 / 62 = 11/31

b) P(male and B) = 9/62

c) P(male or B) = P(male) + P(B) - P(male and B)

                         = 19/62 + 22/62 - 9/62

                         = 32/62

                         = 16/31

d) P(C | male) = P(male and C) / P(C) = (2/62) / (22/62) = 2/22 = 1/11