Suppose a genetic trait in Impalas (Aepyceros datoadeni) occurs more often in males. The sex ratio...
Suppose a genetic trait in Impalas (Aepyceros datoadeni) occurs more often in males. The sex ratio in impalas is bout 50 males to 100 females. 80% of males have this trait, but only 15% of females.
(a) What is the probability that a randomly chosen impala will have the trait?
(b) Suppose a randomly picked impala has the trait (i.e., you pick an impala without paying attention to the sex), what is the probability this impala is a female?
Homework Answers
P(male) = 50/(50+100) = 0.3333
P(female) = 100/150 = 0.6667
P(trait | male) = 0.80
P(trait | female) = 0.15
(a) P(a randomly chosen impala will have the trait), P(trait) = P(male and trait) + P(female and trait)
= 0.33333x0.8 + 0.6667x0.15
= 0.36667
(b) Bayes' Theorem: P(A | B) = P(A and B)/P(B)
P(female | trait) = P(female and trait)/P(trait)
= (0.66667x0.15)/0.36667
= 0.2727
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