SOLUTION: Among 60-year-old college professors, 5% are smokers and 95% are non-smokers. The probability of a non-smoker dying in the next year is 0.005 and the probability for smokers is 0

Algebra ->  Probability-and-statistics -> SOLUTION: Among 60-year-old college professors, 5% are smokers and 95% are non-smokers. The probability of a non-smoker dying in the next year is 0.005 and the probability for smokers is 0      Log On


   

Question 1136592: Among 60-year-old college professors, 5% are smokers and 95% are non-smokers. The
probability of a non-smoker dying in the next year is 0.005 and the probability for smokers is
0.05. Given that one of the group of college professors dies in the next year, what is the
conditional probability that the professor is a smoker? Set up both a sample space and probability measure.
Answer by ikleyn(52890) About Me  (Show Source):
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ANSWER.  P = %280.05%2A0.05%29%2F%280.05%2A0.05+%2B+0.95%2A0.005%29 = 0.3448 = 34.48%

Solution 

They want you find the conditional probability  P(dies AND smoker | dies).


By the definition (and according to the common sense) 


    P(dies AND smoker | dies) = P%28dies_AND_smoker%29+%2F+P%28dies%29 = %280.05%2A0.05%29%2F%280.05%2A0.05+%2B+0.95%2A0.005%29 = 0.3448 = 34.48%    ANSWER

Solved.