A recent survey by the cancer society has shown that the probability that someone is a smoker is P (S) = 0.19. They have also determined that the probability that someone has lung cancer, given that they are 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) ?

0.35

0.03

0.02

0.83

Question

Mathematics

Mattie

19 October, 02:32

A recent survey by the cancer society has shown that the probability that someone is a smoker is P (S) = 0.19. They have also determined that the probability that someone has lung cancer, given that they are 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) ?

0.35

0.03

0.02

0.83

+3

Answers (1)

Know the Answer?

Haylie Norris · Answer 1

P (S∩LC) = 0.03

Step-by-step explanation:

We are given that the probability that someone is a smoker is P (S) = 0.19 and the probability that someone has lung cancer, given that they are a smoker is P (LC|S) = 0.158.

Given the above information, we are to find the probability hat a random person is a smoker and has lung cancer P (S∩LC).

P (LC|S) = P (S∩LC) / P (S)

Substituting the given values to get:

0.158 = P (S∩LC) / 0.19

P (S∩LC) = 0.158 * 0.19 = 0.03