Question

Suppose that 5 percent of men and 0.25 percent of women are color blind. A color-blind person is chosen at random. What is the probability of this person being male? Assume that there are an equal number of males and females. What if the population consisted of twice as many males as females?

Answer 1

Answer: Part 1) 0.9524 = 95.24%

Part 2) 0.9756 = 97.56%

Step-by-step explanation:

Part 1) What is the probability of this person being male? Assume that there are an equal number of males and females.

Let's suppose that there are:

Male: 10000

Female: 10000

Color-blind male: 5% of 10000 = 500

Color-blind female: 0.25% of 10000 = 25

Total color-blind people: 500 + 25 = 525

P(male|color-blind) = P(male ∩ color-blind)/P(color-blind) = 500/525 = 0.9524 = 95.24%

Part 2) What if the population consisted of twice as many males as females?

Let's suppose that there are:

Male: 20000

Female: 10000

Color-blind male: 5% of 20000 = 1000

Color-blind female: 0.25% of 10000 = 25

Total color-blind people: 1000 + 25 = 1025

P(male|color-blind) = P(male ∩ color-blind)/P(color-blind) = 100/1025 = 0.9756 = 97.56%