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 she has type A cancer is 1/3. Type A is deadly: four patients out of five diagnosed with type A cancer die within one year. Type B is less dangerous: only one patient out of five diagnosed with type B cancer dies within one year. What is the probability that your patient has type A cancer and suc- cessfully survives it? What is the probability that your patient dies within a year? Suppose that your patient dies in less than one year before you learn the exact type of cancer he has. Given this sad happening, what is the probability that she had type A cancer?
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
A is deadly: four patients out of five diagnosed with type A cancer die within one year.
Type B is less dangerous: only one patient out of five diagnosed with type B cancer
dies within one year.
What is the probability that your patient has type A cancer and suc-
cessfully survives it? What is the probability that your patient dies within a year? Suppose that your patient dies in less than one year before you learn the exact type of cancer he has. Given this sad happening, what is the probability
that she had type A cancer?
(Hint: You want to start off by considering this question: given the information
provided in the story (what those numbers are really about?), which of the two
analytical tools we have covered in class will be more helpful to solve this problem,
a probability table or a probability tree? )
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