Question

Your name: 1. In the 1980s in Canada, 52% of adult men smoked. It was estimated that male smokers had a lifetime probability of 17.2 % of developing lung cancer, whereas a nonsmoker had a 1.3% chance of getting lung cancer during his life a. What is the conditional probability of a Canadian man getting cancer, given that he smoked in the 1980s? (hint: the event is "getting cancer" and the condition is "smoked". Read the question carefully. The conditional probability, Pr(event condition] Pr lagetting cancer smoked], which has been written in the question) b. Calculate the probability that a Canadian man in the 1980s both smoked and eventually contracted lung cancer. (hint: calculate Pr "getting cancer" and "smoked", which is equal to Pr lgetting cancer smoked] x Pr.(smoked). You have already gotten Prlgetting cancer smoked) from a) Focus English (United States) % 4 5 6 E R T Y U G H J K C V M O. *CO N 7 BS LL Bayes' theorem: Pr[B]A]Pr[A] Pr[B PrAB)= theorem for this specific case (hint d. Write Bayes replace A with smoker and replace B with cancer) e. Calculate the probability that a Canadian man in the 1980s would eventually develop lung cancer (hint: calculate Pr (cancerl, which is equal to Pr (cancer smoker)+ Pr.(cancer non-smoker Use Bayes theorem to caloulate the probability that a Canadian man smoke, given that he had been diagnosed with lung cancer. (hint calculate Pr amoker cancer using the Bayes' theorem your wrote for d.) 1 English (United States) E Focus 44 & 3 5 6 7 R T Y U P F H J K C D O. S4 c. Calculate the probability that a Canadian man in the 1980s both did not smoke and never contracted lung cancer. (hint Calculate Pr no cancer" and "non-smoker", which is equal to Pr Ino cancer I non- smoker) x Pr.Inon-smoker), where Pr.(non-smoker) 1-Pr.[smoker], and Pr [no cancer non-smoker) 1-Pricancer non-smoker) Bayes' theorem PrIBIA]PrA PrlAB PrlB d. Write Bayes replace A wth smoker and replace B with cancer theorem for this specific case (hint T Engish (United States) Focus F10 % 6 8 R T Y U C D G H J K V 5 4

Answer 1

(Date: Civea data Ploten Snaolerr p (cancn P(Gater 0.52 P(non smaken) 0.48 0.172 Canles Nan smoter) : 0.013 Alacndy guen plcancer Sat) n the 4ueshon a) 0.172 P (cancer smaker )x Plinater P(smotu cances de OI72 X 0.52 No cates) la) Pnon-smaker plna no cancennon smoter ) x P(na snokor) Now Pno tacen non-Smote) 1-P O172 D.82& O.39 744 0.828 X 6.48 Bayes Theonam Cancer Snaokn P (snotu tancen Smoter P Ccancer) Cancer non Smober Snoker t P C CenCr plcancer) 0.013 172 O. 185 O1834 0 52 X O. 172 PCsmoker lcancar) 0-185