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A survey of people in a given region showed that 20% were smokers. The probability of death due to lung cancer, given that a person smoked, was 10 · times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is 0.006, what is the probability of death due to lung cancer given that a person is a smoker?

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$1 / 140$

$1 / 70$

$3 / 140$

$1 / 10$

answer is C.

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Detailed Solution

S = smoker, S' = Non-smoker, D = death by cancer Using conditional probability, we can write

$\begin{array}{l} P (D) = P (S) P (D / S) or P (S^{'}) P (D / S^{'}) \\ 0.006 = \frac{20}{100} \cdot P (D / S) + \frac{80}{100} \cdot P (D / S^{'}) = \frac{1}{5} \cdot x + \frac{4}{5} \cdot \frac{x}{10} \end{array}$

[Where P(D/S) = x and given P(D/S) = 10·P(D/S')]

$\Rightarrow x = \frac{3}{140}$

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