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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}
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GPT-5 mini
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A = {KL}
Reason: the complement of "Joe plays" is "Joe is not chosen," i.e. the two chosen are Keitaro and Luis. Since the two names are chosen together (order doesn't matter), the only outcome is KL.
Reason: the complement of "Joe plays" is "Joe is not chosen," i.e. the two chosen are Keitaro and Luis. Since the two names are chosen together (order doesn't matter), the only outcome is KL.
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