Question

7) 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. 60% of males have this trait, but only 10% 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?

Answer 1

SOLUTION:

From given data,

7) 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. 60% of males have this trait, but only 10% of females.

Let ,

Male = M

Female = F

Trait = T

P(M) = 50 /(100+50) = 1/3

P(F) = 100 /(100+50) = 2/3

P(T/ M) = 60% = 60/100 = 0.60 and

P(T / F) = 10% = 10/100 = 0.10

(a) What is the probability that a randomly chosen impala will have the trait?

The probability that a randomly chosen impala will have the trait

P(T) = P(T/M) * P(M) + P(T/F) * P(F)

P(T) = 0.60 * (1/3) + 0.10 * (2/3)

P(T) =0.2 + 0.0667

P(T) = 0.2667

(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?

We will find the probability this impala is a female by using Bayes theorem ,

P(F/T) = P(T/F) * P(F) / P(T)

P(F/T) = 0.10 * (2/3) / 0.2667

P(F/T) = 0.2499