joe, keitaro, and luis play tennis. to decide who will play against each other in the first match, they put…

joe, keitaro, and luis play tennis. to decide who will play against each other in the first match, they put their names in a hat and choose two names without looking. what subset of the sample space, a, represents the complement of the event in which joe plays in the first match? o a = {kl} o a = {kj, kl} o a = {kl, lk} o a = {kj, kl, lj}

joe, keitaro, and luis play tennis. to decide who will play against each other in the first match, they put their names in a hat and choose two names without looking. what subset of the sample space, a, represents the complement of the event in which joe plays in the first match? o a = {kl} o a = {kj, kl} o a = {kl, lk} o a = {kj, kl, lj}

Answer

Explanation:

Step1: List sample - space elements

The sample space of choosing 2 names out of Joe (J), Keitaro (K), and Luis (L) is ${JK, JL, KL}$ (where the order of selection doesn't matter in terms of who plays against whom).

Step2: Identify event and its complement

The event that Joe plays in the first - match has elements ${JK, JL}$. The complement of this event is the set of elements in the sample space that are not in the event that Joe plays. So the complement event has the element ${KL}$.

Answer:

A. ${KL}$