Question

identifying the sample space of the complement of an event four swimmers, daniela, camille, brennan, and amy, compete on a relay team. for the first race of the year, daniela begins the relay. the other three swimmers can swim in any order. the sample space, s, for the event is shown below. s = {cba, cab, bac, bca, acb, abc} after the first race, it is determined that camille is a strong finisher and should be the final swimmer in the race. what subset, a, of the sample space represents the complement of the event in which camille is the final swimmer? a = {cba, cab, bca, acb} a = {abc, bac} a = {cba, cab, bac, bca, acb, abc} a = {ab, ba}

Explanation:

Step1: Identify the event

The event is Camille being the final swimmer. In the sample - space notation, the arrangements where Camille is the final swimmer are those ending with 'C'. From the sample space \(S=\{CBA,CAB,BAC,BCA,ACB,ABC\}\), the arrangements with Camille as the final swimmer are \(BAC\) and \(ABC\).

Step2: Find the complement

The complement of an event contains all the elements in the sample space that are not in the event. So, the complement of the event where Camille is the final swimmer consists of the arrangements that do not end with 'C'. These are \(CBA,CAB,BCA,ACB\).

Answer:

A. \(A = \{CBA,CAB,BCA,ACB\}\)