Question

A health study tracked a group of persons for five years. At the beginning of the study, 20% were heavy smokers, 30% light smokers, and 50% nonsmokers. Results of the study showed that light smokers were twice as likely as nonsmokers to die during the five-year study, but only half as likely as heavy smokers. A randomly selected participant from the study died over the five-year period. Calculate the probability that the participant was a heavy smoker.

Answer 1

Let the probability that a non-smoker will die during the next 5 years = P

Then, The probability that a light smoker will die during the next 5 years = 2 P

The probability that a heavy smoker will die during the next 5 years = 4P

We have

20% heavy smoker

30% light smoker

50% no smoker

So expected number of heavy smoker dying during next 5 year = 0.20*4P = 0.8P

expected number of heavy smoker dying during next 5 year = 0.30*2P = 0.6P

expected number of heavy smoker dying during next 5 year = 0.50*P = 0.5P

So total 0.8P+0.6P+0.5P = 1.9P

So probabilty that a randomly slelected participant who died over 5 year period be a heavy smoker = 0.8P/1.9P

= 0.4211