Final answer:
The correct answer is (d) not enough information. To determine the true probability of having cancer after a positive CT scan result, we need additional information such as the specificity and false positive rate, not provided in the question.
Step-by-step explanation:
If the likelihood that a CT scan shows cancer when you actually have cancer is 85%, the probability that you have cancer when given a positive test cannot be determined with the given information alone. This is because we would also need to know the specificity of the test, i.e., the probability that the test correctly identifies someone as not having cancer when they are indeed cancer-free, and the probability of a false positive, meaning the test indicates cancer when there isn't any. The base rate of cancer in the population is only part of the information needed to calculate the probability that one has cancer given a positive test result (also known as the positive predictive value).
To find the answer, we would use Bayes' theorem which requires not just the sensitivity of the test (here given as 85%) and the base rate of cancer (1%), but also the specificity and the false positive rate.