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

Answer

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. ${KL}$