Consider a collection of $N+1$ urns, numbered $0,1,2,..N$ , each containing a total of $N$ red and white balls.The urn number $K$ has $K$ red and $N-K$ white balls .$(K=0,1,...N)$.An urn is chosen at random and $n<N$ random drawings are made from it by without replacement .What is the conditional probability that all the $n$ balls drawn are taken from the $N$th urn given that they are all red?
I am defining $3$ events: $E_1$: AN urn is chosen at random and $n$ drawings are made
$E$:All balls come out to be red
$E_2$:The $N$th urn is chosen.
We need $P(E_2|E)$.
But I can't evaluate this.