At the beginning of a certain study of a group of persons, 15% were classified a

Question

At the beginning of a certain study of a group of persons, 15% were classified as heavy smokers, 30% as light smokers, and 55% 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. The death rate for nonsmokers is 0.06. A randomly selected participant died over the five-year period; calculate the probability that the participant was a nonsmoker. Round your answer to the nearest 0.001.

Explanation / Answer

death rate of heavysmokers =5*0.06 =0.30

death rate of lightsmokers =3*0.06 =0.18

hence probability of death =P(heavy smoker and died+light smoker and died+non smoker and died)

=0.15*0.30+0.30*0.18+0.55*0.06=0.132

hence probability of participant was nonsmoker given died =P(non smoker and died)/P(died) =0.55*0.06/0.132

=0.25

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