Question

hey, i'd really appreciate some help with this question:
A medical treatment is successful 75% of the time. A hospital wishes to treat a group of patients. How many patients should they take so that the probablity that all are cured is 1/10?

I know that p=0.75 and q=0.25 but i think i need to find n next to solve it but i'm not sure how i can find what n is equal to...

Answer 1

Yes, you will need to find n.

Since P(x) = 0.1 and x = n, you can solve for n using logarithms and the binomial probability function:

P(x) = (nCx)(p^x)[q^(n-x)]

Using what is known:
0.1 = (1)(0.75^x)(0.25^0)

Using logarithms, solve for n:

log(0.1) = n log(0.75)
log(0.1)/log(0.75) = n
8 = n

To check:
P(8) = (8C8)(0.75^8)(0.25^0)
P(8) = 0.1

I hope this will help.