I am leading with the following probability problem:
"The percentage of fails in a subject is 60%. If we know that in a sample of 20 pupils at least 8 of them have failed the exam, which is the probability of having less than 15?"
I have taken the probability of 0.6 and, given X="number of fails", thought of computing $p(8\leq X\leq14)$ in the sample using binomial distribution. In this way, for example: $$p(8)=\binom{20}{8}0.6^80.4^{12}$$ but the sum of all of them is $0.8533$, while the solution must be $0.8717$. I know I am applying something in a wrong way, but don't know what? Appreciate some help. Thanks.