Question

A recent survey by the American Cancer Society shows that the probability that someone is a smoker is P(S) = 0.19. It has also determined that the probability that someone has lung cancer, given that he or she is a smoker, is P(LC|S) = 0.158. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S ∩ LC)?
0.03
0.83
0.35
0.02

Answer 1

P(LC / S) = P(S intersect LC) / P(S)
P(S intersect LC) = P(S)*P(LC / S) = 0.19 * 0.158 = 0.03