Question

At the beginning of a study of individuals, 10% were classified as heavy smokers, 20% were classified as light smokers, and 70% were classified as nonsmokers. In the five-year study, it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively. A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.

Answer 1

Answer: 0.39

Explanation:

Given the following classification :

Heavy smokers (H) = 10%

Light smokers (L) = 20%

Non smokers (N) = 70%

Given that :

The death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively

Let probability of death = D

P(D | N) = d

P(D | H) = 5d

P(D | L) = 3d

Hence,

P(D) = [P(H) * P(D | H) + P(L) * P(D | L) + P(N) * P(D | N)]

P(D) = [0.1 * 5d + 0.2 * 3d + 0.7 * d]

P(D) = [0.5d + 0.6d + 0.7d]

P(D) = 1.8d

A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.

P(N | D) = [P(N) * P(D | N)] / P(D)

P(N | D) = 0.7d / 1.8d

P(N | D) = 0.3888

= 0.39