I'm studying for my stat midterm and I got stuck on this problem. Could anyone give me some feedback?
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 has 17 patients 55 and older and 12 patients younger than 55. A subgroup of 4 patients are chosen and the drug is administered to each. What is the probability that the drug works in all of them?
The answer is supposedly 1.52%.
I made a tree diagram, W = drug works, 55+ = over 55, 55- = under 55, and determined that P(W) = P(W|55+)P(55+) + P(W|55-)P(55-) = .353
I then took .353^4 to get 1.553% but apparently this answer is wrong. How do I get the correct answer?