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, cap A , represents the complement of the event in which Joe plays in the first match?
Answer
A
cap A is equal to KL comma LK
B
cap A is equal to KJ comma KL
C
cap A is equal to KJ comma KL comma LJ
D
cap A is equal to KL
Explanation
The first two names drawn determine the players in the match, and the order of the draws can be recorded. The outcomes in which Joe plays include J, so the complement contains only outcomes with Keitaro and Luis. Those ordered outcomes are KL and LK, which is choice A.
AI-written and checked against the verified answer.