Question

(a) You are a physician meeting with a patient who has just been diagnosed with cancer. You know there are two mutually exclusive types of cancer that the patient could have: type A and type B. The probability that he or she has A is 1/3 and the probability that he or she has B is 2/3. Type A is deadly: four patients out of five diagnosed with type A cancer die (D) within one year. Type B is less dangerous only one patient out of five diagnosed with type B cancer dies (D) within one year. i. Compute the probability that your patient dies within one year. (6 points) ii. Suppose that your patient your patient dies in less than one year, before you learn whether he or she has type A or type B cancer. Given that the patient died in less than a year, what is the probability that she had type A cancer?

Answer 1

summary:

I) P(D) = 2/5 = 0.40

II) P(patient had type A cancer given that she /he died within one year) = 2/3 = 0.66