3.2 Exercise 35

The probability that someone develops cancer during their lifetime is 0.4567. The probability that a person has at least one false positive test result (meaning the test comes back for cancer when the person does not have it) is 0.51. Some of the following questions do not have enough information for you to answer them. Write “not enough information” for those answers. Let C = a person develops cancer and P = person has at least one false positive.

1. $P \left(C\right) =$ ______
2. $P \left(\right. P \left|\right. C \left.\right) =$ ______
3. $P \left(\right. P \left|\right. C' \left.\right) =$ ______
4. If a test comes up positive, based upon numerical values, can you assume that person has cancer? Justify numerically and explain why or why not.