Question

Suppose that a drug is known to be 90% effective in treating a certain disease. What is the probability that it will be successful in treating seven to ten out of 12 patients with the disease?

Answer 1

Probability of treating r number of patients successfully:

P(r) = (nCr)(p^r)(q^r)

Where n = Total number of patients = 12
p = probability of success = 0.90 (90%)
q = probability of failure = 0.10 (10%)

Take the different probabilities for r = 7,8,9,10 and add them up for the answer.

Answer 2

and
nCr = n!/[(n-r)! r! ] the binomial coefficient