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Exercise 13

Avg difficulty 3.0

Eye color, Part I. A husband and wife both have brown eyes but carry genes that make it possible for their children to have brown eyes (probability 0.75), blue eyes (0.125), or green eyes (0.125).

  1. What is the probability the first blue-eyed child they have is their third child? Assume that the eye colors of the children are independent of each other.

  2. On average, how many children would such a pair of parents have before having a blue-eyed child? What is the standard deviation of the number of children they would expect to have until the first blue-eyed child?

Diez, Barr & Çetinkaya-Rundel, OpenIntro Statistics, Distributions of random variables, End-of-Chapter Exercises, Exercise 13

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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.