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?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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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Follow-up Question

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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