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3 March, 04:41

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?

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  1. 3 March, 05:02
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    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%
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