At the beginning of a certain study of a group of persons 15

\"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 smokers and light smokers were seven and three times that of the nonsmokers, respectively. A randomly selected participant died over the five-year period. What is the probability that the participant was a nonsmoker?\"

I\'m really confused about the \"7 times more likely and 3 times more likely to die\". Please help.

Solution

Let:

H :Event of a heavy smoker

L: Event of a light smoker

N : Event of a non-smoker

D : Event of a death within five-year period

Now we are given that , P [D/H] = 7 P[D/N] and P [D/L] = 3 P[D/N]

According to Bayes Theoram:

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

=P[D/N]*0.55 / ( P[D/N]*0.55+ 7P[D/N]*0.15+ 3P[D/N]*0.3)

=P[D/N]*0.55 / P[D/N](0.55+ 7*0.15+ 3*0.3)

=0.55 /(0.55+ 7*0.15+ 3*0.3)

=0.22 Answer