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?

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)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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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