Question

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? a = {kl} a = {kj, kl} a = {kl, lk} a = {kj, kl, lj}

Explanation:

Step1: List all possible pairs

The sample - space of choosing 2 names out of 3 (Joe - J, Keitaro - K, Luis - L) is $\{KJ, KL, LJ\}$.

Step2: Identify the event of Joe playing

The event of Joe playing consists of pairs with J: $\{KJ, LJ\}$.

Step3: Find the complement

The complement of the event of Joe playing is the pair without J, which is $\{KL\}$.

Answer:

A. $\{KL\}$