You are working for an agency that is in charge of protectin

You are working for an agency that is in charge of protecting the United States against an Ebola epidemic and wonder whether you should screen or quarantine passengers from certain countries. The probability that any given passenger has Ebola is one in a million. The probability that he is traveling from Liberia if he has Ebola is 0.9. Overall, one in 10,000 passengers is traveling from Liberia. What is the probability that a passenger has Ebola if he is traveling from Liberia? A. 0.1 B. 0.2 C. 0 D. 0.01 E. 0.05

Solution

Let

E = has Ebola
L = from Liberia

Thus,

P(E|L) = P(E) P(L|E) / P(L)

= (1/1000000)*(0.9) / (1/10000)

= 0.009 = 0.01 [ANSWER, OPTION D]