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?

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

Step-by-step 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