Exercise 4 — Candidates who have followed the speciality course We have two urns $U$ and $V$ each containing two balls. Initially, urn $U$ contains two white balls and urn $V$ contains two black balls. We perform successive draws from these urns as follows: each draw consists of taking at random, simultaneously, one ball from each urn and putting it in the other urn. For any non-zero natural number $n$, we denote by $X_n$ the random variable equal to the number of white balls in urn $U$ after $n$ draws.
\textbf{Exercise 4 — Candidates who have followed the speciality course}
We have two urns $U$ and $V$ each containing two balls. Initially, urn $U$ contains two white balls and urn $V$ contains two black balls.\\
We perform successive draws from these urns as follows: each draw consists of taking at random, simultaneously, one ball from each urn and putting it in the other urn.\\
For any non-zero natural number $n$, we denote by $X_n$ the random variable equal to the number of white balls in urn $U$ after $n$ draws.