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:A=OPMN, OMPN

Step-by-step explanation:

we know oliver is first in the race and naim is last so the other racers are in between

A = {MOPN, MPON, PMON, POMN}

Step-by-step explanation:

Everyone has already agreed that Naim would be the last skater, so we have to make sure that the result has 'N' in each last place. As we can see, they all have this.

Now, we also have to make sure Oliver not first, because although they're trying to decide, the problem asks for the complement in which "Oliver is the first skater in the race."

A complement is all the values that are NOT in the set, so it cannot be A = {OPMN, OMPN) or A = {MOPN, MPON, OPMN, POMN), because they both have at least one case where 'O' is first.

A complement is ALL other values of the set, so it cannot be A = {MOPN, PMON}, because that set only shows two possible values.

Therefore, A = {MOPN, MPON, PMON, POMN} is your answer.