Question

A pharmaceutical company claims that a new drug is successful in relieving arthritic pain in 70% of patients. Suppose that the claim is correct. The drug is given to 10 patients. What is the probability that 8 or more patients experience pain relief?

Answer 1

`0.3828~~38.3%`

Explanation:

`P["k on 10 patients are relieved"] = C(10,k) (7/10)^k (3/10)^(10-k)`
`"with "C(n, k) = (n!)/(k! (n-k)!)" (combinations)"`
`"(binomial distribution)"`

`"So for k=8, 9, or 10 , we have :"`

`P["at least 8 on 10 patients are relieved"] =`
`(7/10)^10 (C(10,10) + C(10,9) (3/7) + C(10,8) (3/7)^2)`
`= (7/10)^10 (1 + 30/7 + 405/49)`
`= (7/10)^10 (49 + 210 + 405)/49`
`= (7/10)^10 (664)/49`
`= 0.3828`

`~~38.3%`