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

Question

A B C Total

Male 4 11 15 30

16 10 18 44

20 21 33 74

If one student is chosen at random,

Find the probability that the student was female:   

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

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

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

Answer 1

(A) P(female) = 44/74

(B) P(female ∩ “A”) = 16/74

(C) P(female ∪ “A”) = P(female) + P(“A”) - P(female ∩ “A”)

= 44/74 + 20/74 - 16/74

= 48/74

(D) P(female | “A”) = P(female ∩ “A”)/P(“A”)

= (16/74)/(20/74)=16/20

*If your teacher requires you to reduce your fraction answers then do so. Most teachers like it non-reduce so they can identify the number of favorable outcomes and the total possible outcomes.