Question

Giving a test to a group of students, the grades and gender are summarized below. Round your answers to 4 decimal places.

Grades and Gender

	A	B	C	Total
Male	3	4	9	16
Female	10	5	17	32
Total	13	9	26	48

If one student is chosen at random,

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

b. Find the probability that the student was male AND got an "A": ________

c. Find the probability that the student was male OR got a "C": _________

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

Answer 1

a) P(C) = 26/48 = 0.5417

The probability that the student got a C is 0.5417

b) P(male AND A) = 3/48 = 0.0625

The probability that the student was male AND got an "A" is 0.0625

c) P(male OR C)

= P(male) + P(C) - P(male AND C)

= (16/48) + (26/48) - (9/48)

= (16 + 26 - 9) / 48

= 33/48

= 0.6875

The probability that the student was male OR got a "C" is 0.6875

d) P(C | male ) = 9/16 = 0.5625

If one student is chosen at random, the probability that the student got an 'C' GIVEN they are male is 0.5625