1 . Let $\pi_1,\ldots,\pi_{20}$ be a random permutation of $\{1,\ldots,20\}$. Define the events:
$ A = \pi_{10}>\pi_{11} $
and
$ B = \pi_{11} \gt \pi_{12} $
Which of the following is true?
(a)
$\Pr(A\cap B) < \Pr(A)\cdot\Pr(B)$
(b)
None of the above
(c)
$\Pr(A\cap B) = \Pr(A)\cdot\Pr(B)$
(d)
$\Pr(A\mid B)$ is undefined
(e)
$\Pr(A\cap B) > \Pr(A)\cdot\Pr(B)$