Is there a way to find the probability p with R for pbinom

Question

I think this is a rather common problem, but I could not find a solution.

I want to solve the following equation: pbinom(18,25,p)=0.05.

Is there a way to find the unknown p with the program R?

Every help is appreciated.

Answer 1

Root finding:

print(
  res <- uniroot(function(p) pbinom(18,25,p) - 0.05, c(0, 1), 
          tol = .Machine$double.eps)
)

pbinom(18,25,res$root)
#[1] 0.05

Answer 2

Brute force :

p = 0.0001 # starting point
while (abs(pbinom(18,25,p) -  0.05) > 0.001) p <- p + 0.001

This code evaluates the pdf for different values of p until you are "close enough" to 0.05. Here "close enough" means at the 0.001 range.

> p
[1] 0.8601
> pbinom(18,25,0.8601)
[1] 0.05070763