Question

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

Answer 1

the probability of having sickle cell anemia given that you are African-American is P( B|A) =0.288

Explanation:

Using Bayes's theorem

P( B|A) = P( A∩B)/P(A)

where P( B|A) = probability of the event B knowing that A happened , P( A∩B) = probability that A and B happen (joint probability of A and B) , P(A) = probability of event A

if B= probability of having sickle cell anemia and A= probability of being African-American

then

P( A∩B) = 0.13

P(A) = 0.45

then

P( B|A) = P( A∩B)/P(A) = 0.13/0.45 = 0.288

P( B|A) =0.288