probability and stats

Question

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

A	B	C	Total
Male	17	13	14	44
Female	16	6	4	26
Total	33	19	18	70

If one student is chosen at random,

Find the probability that the student got a B:   

Find the probability that the student was female AND got a "B":   

Find the probability that the student was female OR got an "C":   

If one student is chosen at random, find the probability that the student was male GIVEN they got a 'A':   

Answer 1

A = grade of "A"

B = grade of "B"

C = grade of "C"

P(B) = 19/70 = 0.2714

The probability that the student got a "B" on the test is 0.2714.

P(Female ∩ B) = 6/70 = 0.08571

The probability that the student is a female and got a "B" on the test is 0.08571

P(Female ∪ C) = P(Female) + P(C) - P(Female ∩ C) = (26/70) + (18/70) - (4/70) = 40/70 = 4/7 = 0.5714

The probability that the student is either a female or got a "C" on the test is 0.5714.

P(Male|A) = P(Male ∩ A) ÷ P(A) = (17/70) / (33/70) = (17/70)*(70/33) = 17/33 = 0.5152

The probability that the student who got a "A" on the test is a male is 0.5152.