A new drug for leukemia works 25% of the time in patients 55 and older, and 50% of the time in patients younger than 55.  A test group consists of 17 patients 55 and older and 12 patients younger than 55.

(a) A patient is chosen uniformly at random from the test group, the drug is administered, and it is a success.  What is the probability the patient was in the older group?

(b) A subgroup of 4 patients are chosen and the drug is administered to each.  What is the probability that the drug works in all four patients?

[Author Mark Huber. Licensed under Creative Commons.]