Probabibility and combinatorics

Question

Of 100 patients with a certain disease, 10 were chosen at random to undergo a drug treatment that increases the cure rate from 50% for those not given the treatment to 75% for those given the drug treatment.

a. What is the probability that a randomly chosen patient both was cured and was given the drug treatment?

b. What is the probability that a patient who was cured had been given the drug treatment?

c. What is the probability that a specific group of 10 patients was chosen to undergo the drug treatment? (Leave your answer in terms of factorials.)

Answer 1

Hi Nick M.,

Problem is ambiguous whether the random chosen group for treatment is the same random chosen population for part (a).

I'll assume not.

So set up your groups -- of the 90 not treated, 45 are cured; of the 10 treated, 7.5 are cured. (Don't worry about the fraction!)

You can just sit and tote up your sets.

So for (a), it's just 7.5/100 . Those 7.5 were both cured and treated!

For (b), it's 7.5/(7.5+45) . 7.5 were treated and cured, and (7.5 + 45) were cured.

For (c), it's a combination of 10 (the order you pick them in doesn't matter, so it's not a permutation) from a population of 100. You should know the formula for that, by now ...

-- Cheers, --Mr. d.