Question

In a population of elderly war veterans, the probability that a veteran will have been exposed to agent orange (a militarized herbicide) and develop cancer is 0.35. The probability is 0.75 that a veteran exposed to agent orange will develop cancer. The average age of the veterans is 67 years old. What is the probability that a random veteran will have been exposed to agent orange

Answer 1

Probability that a random veteran will have been exposed to agent orange is 0.4667

Explanation:

P(exposed to agent cancer and develop cancer) = 0.35

P(develop cancer given he is already exposed to agent orange) = 0.75

P(is exposed to agent cancer) = ?

P(A given B) = P(A and B)/P(B),

P(develop cancer | exposed to agent orange) = P(develop cancer and exposed to agent orange)/P(exposed to agent orange)

0.75 = 0.35/P(exposed to agent orange)

P(exposed to agent orange) = 0.35/0.75

P(exposed to agent orange) = 0.4667