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  • 25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smok

25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is \frac{k}{10} . Then the value of k is.

Option: 1

9


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

$$ \begin{aligned} & \mathrm{P}(\text { smoker })=\frac{1}{4} \\ & \mathrm{P}(\text { non smoker })=\frac{3}{4} \end{aligned}
Probability that a smoker has lung cancer
$$ \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{S}}\right)=27 \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{NS}}\right)
Probability that a person is smoker when he has lung cancer
$$ \begin{aligned} & =\frac{P(S) \cdot P\left(\frac{C}{S}\right)}{P(S) \cdot P\left(\frac{C}{S}\right)+P(N S) \cdot P\left(\frac{C}{N S}\right)} \\ & =\frac{\frac{1}{4} \times P\left(\frac{C}{S}\right)}{\frac{1}{4} \times P\left(\frac{C}{S}\right)+\frac{3}{4} P\left(\frac{C}{N S}\right)} \\ & =\frac{\frac{1}{4} \times 27 \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{NS}}\right)}{\frac{1}{4} \times 27 \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{NS}}\right)+\frac{3}{4} \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{NS}}\right)} \\ & \frac{27}{30}=\frac{\mathrm{k}}{10} \\ & \mathrm{k}=9 \end{aligned}

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