Question

Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last skater. Then, they try to decide whether or not Oliver should be the first skater in the race.

Which subset, A, of the sample space shows the complement of the event in which Oliver is the first skater in the race?

A = {MOPN, PMON}
A = {OPMN, OMPN}
A = {MOPN, MPON, OPMN, POMN}
A = {MOPN, MPON, PMON, POMN}

Answer 1

With N fixed last, the sample space (first three positions) is the 6 permutations of M, O, P:
MOPN, MPON, OMPN, OPMN, PMON, POMN.
The event "Oliver is first" is {OMPN, OPMN}, so its complement is the other four:
A = {MOPN, MPON, PMON, POMN}.