In a population, 50% do not smoke, 20% are light smokers, and 30% are heavy smokers. Heavy smokers are twice as likely to die as light smokers, and light smokers are twice as likely to die as non-smokers. What is the probability that a person was a heavy smoker given that they have died?

Free worked solution · Quant Blueprint

4/7, approximately 57.14%.

1. Let the death probability for a non-smoker over the specified period be d. Light and heavy smokers then have probabilities 2d and 4d.
2. The weighted death probability is 0.5d + 0.2(2d) + 0.3(4d) = 2.1d.
3. Heavy-smoker deaths contribute 1.2d. Bayes’ rule gives P(heavy | died) = 1.2d/(2.1d) = 4/7. The unspecified baseline cancels.

Common mistake

The 30% population share is a prior probability. Observing a death changes the relative weights; heavy smokers are overrepresented in the conditioned group.

Follow-up

Among those who died, non-smokers have share 5/21 and light smokers 4/21. Together with 12/21 for heavy smokers, the shares sum to one.

Original educational explanation for this practice question. Reviewed 2026-10-13. Firm-style practice; the label describes the collection’s preparation context.