Suppose in a class of $20$ students $25$% know Java .If we take a random sample of $5$ students,then What is the probability that exactly $2$ of them know Java ?
Well, I thought Binomial distribution is perfect for this.
$C(5,2) * (0.25)^2 * (0.75)^3= 0.263$
Even, I thought to use Hypergeometric distribution here,
$\frac{C(5,2) * C(15,3)}{C(20,5)} = 0.29$
Why is there such a difference ?
Hypergeometric distribution assumes that students are picked without replacement whereas Binomial distribution assumes that students are picked with replacement
Hypergeometric distribution is the correct one to use here