Question

Let `X` be a binomial random variable with `p=0.3` and `n=15`. What is `P(X>9)`?

Answer 1

`0.3%`

Explanation:

Here we can use the cmf to solve, stated as

`sum_k^n ((n!)/(k!(n-k)!)) p^k (1-p)^(n-k)`

so now

`sum_(k=10)^15 ((15!)/(k!(15-k)!)) .3^k (1-.3)^(15-k)`

the answer is around `.3%`

intuitively if we only have a .3 probability then getting 10 or more out of 15 should be relatively impossible.