Question

2.20 Assortative mating: Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 217 Scandinavian men and their female partners. The table below summarizes the results (rows represent male eye color while columns represent female eye color). For simplicity, we only include heterosexual relationships in this exercise.
(please round any numerical answers to 4 decimal places)

	Blue	Brown	Green	Total
Blue	52	24	23	99
Brown	16	22	15	53
Green	18	14	33	65
Total	86	60	71	217

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?
b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?
d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?
e) Does it appear that the eye colors of male respondents and their partners are independent? Explain.

• No, it is much more likely for a male with blue eyes to have a blue-eyed partner than it is for a male with any other eye color
• Yes, people don't choose spouses based on eye color

Answer 1

a)

probability that a randomly chosen male respondent or his partner has blue eyes

=(86+99-52)/217 =0.6129

b)

probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes

=(52/99) =0.5253

c)

probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes =(16/53) =0.3019

d)

probability of a randomly chosen male respondent with green eyes having a partner with blue eyes =(18/65)=0.2769

e)

No, it is much more likely for a male with blue eyes to have a blue-eyed partner than it is for a male with any other eye color