Question: 2019 Winter Final - 17
Let $n \geq 8$ be an integer. Consider a uniformly random permutation $a_1,a_2,...,a_n$ of
the set $\{1,2,...,n\}$. Consider the events
- A = "$a_7$ is the minimum of $a_1,a_2,...,a_7$",
- B = "$a_6$ is the minimum of $a_1,a_2,...,a_6$".
(a)
The events $A$ and $B$ are not independent.
(b)
None of the above.
(c)
All of the above.
(d)
The events $A$ and $B$ are independent.