Doctors report that the probability of developing (lung) cancer given a person s

Question

Doctors report that the probability of developing (lung) cancer given a person smokes is 0.8 and the probability of developing lung cancer if a person doesn’t smoke is 0.2.

Assume 25% of the population smokes.

a: Determine the probability that a person develops lung cancer.

b: Determine the probability that a person smokes given they have lung cancer.

Hello, this is a problem from course Probability and Random Processes. Please do the problem step by step and take a sharp picture of the solution. Thank you.

Explanation / Answer

a. P(Person develops lung cancer) = P(person smokes)*(P(developing lung cancer/person smokes) + P(person doesnt smoke)*(P(developing lung cancer/person doesnt smoke)

= 0.25*0.8 + (1-0.25)*0.2

= 0.2 + 0.15

= 0.35

b. P(person smokes/lung cancer) = P(person smokes and has lung cancer) / P(person has lung cancer)

= 0.25*0.8 / 0.35 (from a)

= 0.5714

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