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**aptremblay** A cohort study is done to assess the impact of smoking on lung cancer. In this study, a large representative sample of first year university students are followed for 40 years. For each student, the smoking status is recorded as well as the lung cancer status at the end of the follow-up period. In the cohort, 20% of students smoked and among those, 50%developed lung cancer. Among the remaining students, 6.25% developed lung cancer.

a) Compute the probability of developing a cancer.

b) Is developing lung cancer independent of smoking? why?

c) Using Bayes' rule, compute the conditional probability of smoking given the development of a lung cancer.