Question

1.      Assume that the probability of having sickle cell anemia is 0.15 and the probability of being African-American is 0.45 in a given population. Additionally, assume the joint probability of having sickle cell anemia and being African-American in this population is 0.13.

A) What is the probability of having sickle cell anemia, given that you are African-American in this given population?

B) Suppose we know that the probability of having sickle cell anemia, given that you are Asian-American is 0.21. What can we say about the relative risk of sickle cell anemia in African-Americans versus Asian Americans? Interpret this result.

Answer 1

A)

Let P(S) be the probability of having sickle cell anemia and let P(A) be the probability of being African-American.

Then P(S) = 0.15, P(A) = 0.45 and P(S A) = 0.13

The probability of having sickle cell anemia, given that you are African-American =

P(S | A) = P(S A) / P(A) = 0.13 / 0.45 = 0.2889

B)

Let P(B) be the probability of being Asian-American

Given, P(S | B) = 0.21

The relative risk of sickle cell anemia in African-Americans versus Asian Americans =

P(S | A) / P(S | B) = 0.2889 / 0.21 = 1.3757

African-Americans have 1.3757 times risk of getting sickle cell anemia than Asian-American.