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

Apr 26, 2017

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.