Question

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 203 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.
(Round any numerical answers to 4 decimal places if possible.)

Fem BlueFem BrownFem GreenTotal

Male Blue582815101

Male Brown1624848

Male Green18122454

Total926447203

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 female respondent has blue eyes given that her partner has blue eyes?
c) What is the probability that a randomly chosen female respondent has blue eyes given that her partner has brown eyes?
d) What is the probability of a randomly chosen female respondent has blue eyes given that her partner has green 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

	fem blue	fem brown	fem green	total
male blue	58	28	15	101
male brown	16	24	8	48
male green	18	12	24	54
total	92	64	47	203

a)

P( male respondent or his partner has blue eyes =(101+92-58)/203=135/203=0.6650

b)

probability that a randomly chosen female respondent has blue eyes given that her partner has blue eyes =58/101 =0.5743

c)

probability that a randomly chosen female respondent has blue eyes given that her partner has brown eyes =16/48 =0.3333

d)

probability of a randomly chosen female respondent has blue eyes given that her partner has green eyes =18/54 =0.3333

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