IMathAS-libretexts

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4.23 Eye color, Part II: A previous exercise 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?
(please round to four decimal places)

(b) What is the probability that exactly one of their two children will have green eyes?
(please round to four decimal places)

(c) If they have six children, what is the probability that exactly two will have green eyes?
(please round to four decimal places)

(d) If they have six children, what is the probability that at least one will have green eyes?
(please round to four decimal places)
(e) What is the probability that the first green eyed child will be the 4th child?
(please round to four decimal places)
(f) Would it be considered unusual if only 2 out of their 6 children had brown eyes?

No, the probability of having at most two children with brown eyes exceeds 5%
No, the probability of having exactly two children with brown eyes is less than 5%
Yes, the probability of having at most two children with brown eyes is less than 5%
Yes, there are relatively few options here, so all are likely

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