Question

Of all college degrees awarded in the US,
26% of all degrees awarded are Associate degrees
40% of all degrees are earned by males
10% are of all degrees awarded are Associate degrees earned by males.

1a) Sketch a Venn Diagram.
1b) What % of all degrees awarded are associate degrees earned by women?
1c) What % of women earn a college degree other than an Associate degree?
1d) What percent of all degrees are earned by women?
1e) What is conditional probability that a degree earned by a man, given that it is an Associate degree?

Answer 1

1a) Let A indicate the event that a degree awarded is an Associates degree and M indicate the event that the degree is earned by a male.

Venn Diagram

1b) Percentage of all degrees awarded that are associate degrees earned by women = 16%

1c) Percentage of women that earn a college degree other than an Associate degree = 44%

1d) Percentage of all degree earned by women = 16 + 44 = 60%

1e) P(M | A) = P(M & A)/P(A) [Bayes' Theorem: P(A | B) = P(A & B) / P(B)]

= 0.10/0.26

= 0.3846