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Exercise 23

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Eye color, Part II. Exercise 4.13 introduces a husband and wife with brown eyes who have 0.75 probability of having children with brown eyes, 0.125 probability of having children with blue eyes, and 0.125 probability of having children with green eyes.

  1. What is the probability that their first child will have green eyes and the second will not?

  2. What is the probability that exactly one of their two children will have green eyes?

  3. If they have six children, what is the probability that exactly two will have green eyes?

  4. If they have six children, what is the probability that at least one will have green eyes?

  5. What is the probability that the first green eyed child will be the 4th4^{th} child?

  6. Would it be considered unusual if only 2 out of their 6 children had brown eyes?

Diez, Barr & Çetinkaya-Rundel, OpenIntro Statistics, Distributions of random variables, End-of-Chapter Exercises, Exercise 23

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Adapted from OpenIntro Statistics © 2019 David Diez, Mine Çetinkaya-Rundel & Christopher D. Barr. Licensed under CC BY-SA 3.0. Source: OpenIntro Statistics. Imported at revision fee2509.