Suppose that 5% of men and 0.25% of women are color-blind from a population that is 50% men and 50% women. (a)  A person is chosen at random, and that person is color-blind. What is the probability that the person is male? (b)  A person is chosen at random, and that person is not color-blind. What is the probability that the person is male? (c)  Two people are chosen at random, and they are both color-blind. What is the probability they are the same gender?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Suppose that 5% of men and 0.25% of women are color-blind from a population that is 50% men and 50% women.

    1. (a)  A person is chosen at random, and that person is color-blind. What is the probability that the person is male?

    2. (b)  A person is chosen at random, and that person is not color-blind. What is the probability that the person is male?

    3. (c)  Two people are chosen at random, and they are both color-blind. What is the probability they are the same gender?

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For 3c why is my approach incorrect? 

1 - [ P(male | colorblind) * P(female | colorblind) ]

1 - [P(E1|A) * P(E2|A)] = 1 - [0.9524 * (1-0.9524)] = 0.9547

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