Binomial law problem

Question

We have 25 persons, 11 women and 14 men. We chose 5 people at random. X represent the number of women chosen

I'm pretty sure that this is a binomial theorem problem.

It asks for the variance :

var = npq

where

n : number of times the experiment is done

p : probability of success

q : probability of failure

var = 5 * (11/25) * (14/25) = 1,232

Seems wrong according to manual. Any help ?

Answer 1

I'm pretty sure that this is a binomial law problem.

It is not.   You are not counting the success among a finite sequence of independent and identically distributed selections.   The selections are definitely codependent.

You are selecting a sample of size $n=5$ from a population of size $N=25$ with a known amount of favoured items $K=11$.   The count of women in the sample will have an hypergeometric distribution.

$$Y\sim \mathcal{Hyp}(N,K,n)\\[1ex] \mathsf{Var}(Y) = \dfrac{n K}{N}\dfrac{N-K}{N}\dfrac{N-n}{N-1}$$

Answer 2

You should check your math again: $\ 5 \cdot \frac{11}{25}\cdot\frac{14}{25} \neq \ 1,232$

Also, I think you should look into the Binomial theorem further to get a better understanding of it and when to use it.