1 .
Let $n \geq 3$ be an integer. Consider a uniformly random permutation $a_1a_2 \dots a_n$ of the set
$\{1,2,\dots,n\}$. Define the events
- A = "$a_n = n$",
- B = "$a_2 > a_1$".
(a)
The events $A$ and $B$ are independent.
(b)
None of the above.
(c)
The events $A$ and $B$ are not independent.