Question

A doctor studies the known cancer patients in a certain town. The probability that a randomly chosen resident has cancer is found to be 0.0019. It is found that 28% of the town works for Ajax Chemical Company. The probability that an employee of Ajax has cancer is equal to 0.0019. Are the events "has cancer" and "works for Ajax" independent of one another?

Yes or No

Answer 1

Let the event 'has cancer' be C, and the event 'works for Ajax' be A.
P(C) = 0.0019. P(A) = 0.28
The events A and C are independent if P(C|A) = P(C).
P(C|A) = 0.0019 = P(C).
Therefore the answer is YES.