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 rate of heavy smokers was 75%, the death rate of light smokers was 45%, and the death date of non-smokers was 15%.

Draw a tree diagram for this situation

A randomly selected participant managed to survive throughout the five-year period of the study.. Calculate the conditional probability that the participant was a nonsmoker.

Answer 1

a) The tree diagram for the given states and probabilities here is obtained as:

Using the law of total probability, we get here:
P(alive) = P(alive | heavy smoker)P(heavy smoker) + P(alive | light smoker)P(light smoker) + P(alive | no smoker)P(no smoker)

P(alive) = 0.15*0.25 + 0.3*0.55 + 0.55*0.85 = 0.67

Now using Bayes theorem , we have here:

P( non smoker | alive ) = P(alive | no smoker)P(no smoker) / P(alive ) = 0.55*0.85 / 0.67 = 0.6978

Therefore 0.6978 is the required probability here.