four speed skaters, marco, naim, oliver, and pedro, compete in a relay race where they all agree that naim…

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?\n\na = {mopn, pmon}\na = {opmn, ompn}\na = {mopn, mpon, opmn, pomn}\na = {mopn, mpon, pmon, pomn}

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?\n\na = {mopn, pmon}\na = {opmn, ompn}\na = {mopn, mpon, opmn, pomn}\na = {mopn, mpon, pmon, pomn}

Answer

Explanation:

Step1: Identify fixed - last skater

Since Naim is the last skater, we only need to arrange the first three positions among Marco, Oliver, and Pedro.

Step2: Define the event

The event we are considering is Oliver being the first skater. The complement of this event is all arrangements where Oliver is not the first skater.

Step3: List non - Oliver first arrangements

When Oliver is not the first skater, the first skater can be Marco or Pedro. If Marco is the first skater, the possible arrangements (with Naim last) are MOPN and MPON. If Pedro is the first skater, the possible arrangements (with Naim last) are PMON and POMN.

Answer:

A = {MOPN, MPON, PMON, POMN}