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Assume that the probability of developing lung cancer in smokers is 15%; the probability of developing lung cancer in non-smokers is 1%; and the prevalence of smokers in the U.S. is 20%. If a person is diagnosed with lung cancer, what is the probability that he/she is a smoker?

Respuesta :

Answer:0.789

Step-by-step explanation:

  20 % person smokes and 80 % don't smoke

Probability that a smoker gets lung cancer=15%

Probability that a non smoker gets lung cancer is =1%

Thus

Probability if a person is diagnosed with cancer he/she is a smoker

P=[tex]\frac{Smoker}{Given he gets cancer}[/tex]

P=[tex]\frac{0.2\times 0.15}{0.8\times 0.01+0.2\times 0.15}[/tex]

P=[tex]\frac{0.03}{0.038}[/tex]=0.789

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