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, lets see all the possible outcomes. since naim is always last, we have to order the rest of the 3. there are 6 ways to do it (two combinations for each when they are the 1st). opmn, ompn, mopn, mpon, pomn, pmon. we can easily see the set b where oliver is first; b= opmn, ompn. the complement of this set is anything that is not in this set. checking our choices, the correct choice for this is the last one; a={mopn, mpon, pomn, pmon}note: (choices 2 and 3 even have oliver as a first skater in a race, so they are dismissed immediately since the complement means that this can't hold).