At the beginning of a study of individuals, 10% were classified as heavy smokers, 20% were classified as light smokers, and 70% were classif

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.

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Kiệt Gia 4 months 2021-08-06T10:04:45+00:00 1 Answers 1 views 0

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    2021-08-06T10:06:12+00:00

    Answer: 0.39

    Step-by-step 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

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