1 .
Let $n \geq 2$ be an integer. You are given $n$ beer bottles $B_1,B_2,...,B_n$ and two cider bottles $C_1$ and $C_2$.
Consider a uniformly random permutation of these $n + 2$ bottles. The positions in this permutation are
numbered $1,2,...,n + 2$. Consider the random variable
- X = the position of the leftmost beer bottle.
(a)
$\frac{n}{n + 2} + \frac{2n + 2}{(n + 1)(n + 2)}$
(b)
$\frac{n}{n + 2} + \frac{2n + 6}{(n + 1)(n + 2)}$
(c)
$\frac{n}{n + 2} + \frac{4n + 2}{(n + 1)(n + 2)}$
(d)
$\frac{n}{n + 2} + \frac{4n + 6}{(n + 1)(n + 2)}$