showed that 20% were smokers. The probability of death due tolung cancer (if you

Question

showed that 20% were smokers. The probability of death due tolung cancer (if you were a smoker) was about 10 times theprobability of death due to lung cancer if you were not a smoker.If the probability of death due to lung cancer in this region is.006, what is the probability of death due to lung cancer given aperson is a smoker? Thanks showed that 20% were smokers. The probability of death due tolung cancer (if you were a smoker) was about 10 times theprobability of death due to lung cancer if you were not a smoker.If the probability of death due to lung cancer in this region is.006, what is the probability of death due to lung cancer given aperson is a smoker? Thanks

Explanation / Answer

P (a person is a smoker) = 0.2 =P(A1) =>P( a person is a non- smoker) = 0.8 =P(A2) P( death due to lungcancer/smoker ),P(E / A1) = 6P( death due to lungcancer/ non smoker ),P(A/E2) and is given that P( death due to lungcancer) = 0.06=P(E) we know, P(E) =P(A1)*P(E/A1) + P(A2)*P(E/A2)                 0.06 = 0.2 *P(E/A1 ) + 0.8 (6*P(A/E1))                         = 0.2P(E/A1 )+ 4.8 P(E/A1 )                      0.06 = 5P(E/A1 ) =>P(E/A1 ) ,P( death due to lung cancer given a personis a smoker) = 0.06 /5 = 0.012

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