Let A and B tow urns containing both N balls numbered from $1$ to $N$.
- 1) We assume to extract casually one ball from A and one ball from B. What is the probability that they have the same number?
$\rightarrow \mathbb{P}($same number at the first extraction$)=\frac{1}{N^2}$
2) We assume to remove from urns the balls extracted only if these balls are equal, and to repeat a second time the extraction. What is the probability to obtain two equal numbers at the second extraction?
3) Knowing that at the second extraction we have obtained tow equal numbers, waht is the probability that even at the first extraction were obtained two equal numbers?
I have difficulty to solve the second point, because for the third point just apply Bayes. Can you help me? Thanks in advance.