3.33 Eye color, Part II. Exercise 3.23 introduces a husband and wife with brown

Question

3.33 Eye color, Part II. Exercise 3.23 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 (a) What is the probability that their first child will have green eyes and the second will not? (b) What is the probability that exactly one of their two children will have green eyes? (c) If they have six children, what is the probability that exactly two will have green eyes? (d) If they have six children, what is the probability that at least one will have green eyes?

Explanation / Answer

a) P(First has green eyes and second not) = 0.125*(1-0.125) = 0.109375

b) P(Exactly has green eyes) = 0.125*(1-0.125)+(1-0.125)*0.125 = 0.21875

c) P(Exactly two have green eyes)

Use Excel function

BINOM.DIST(2,6,0.125,FALSE)

= 0.137386

d) P(At least one have green eyes)

= 1- P(No one has green eyes)

= 1-BINOM.DIST(0,6,0.125,FALSE)

= 0.551205

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