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Question: 2018 Fall Final - 15

Author: Michiel Smid
Consider a uniformly random permutation $a_1,a_2,a_3,a_4$ of the set $\{1,2,3,4\}$. Define the events
  • A = "$a_1 > a_2$",
  • B = "$a_4 > a_3$".
Which of the following is correct?
(a)
None of the above.
(b)
All of the above.
(c)
The events $A$ and $B$ are independent.
(d)
The events $A$ and $B$ are not independent.