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. MPON, PMON, POMN)

Step-by-step explanation:

Complete 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)

So,

Naim would be last, that means, "N" must come last in all the sets. All of them have this, so that's good.

Now, they want "COMPLEMENT" of the set where Oliver is 1st. Complement is the "opposite" event, not in set/subset. So we disregard anyone where there is "O" in first place.

1st set have only 2 possibilities, so that's out.

2nd set have same, so that's out.

3rd set has "O" at first place in third sub, so that's out.

4th set DOESN'T have "O" in first place and has 4 subs, so this is the correct answer.

A = {MOPN. MPON, PMON, POMN)  -- correct