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, A, represents the complement of the event in which Joe plays in the first match?
A) A = {KL}
B) A = {KJ, KL}
C) A = {KL, LK}
D) A = {KJ, KL, LJ}

Answer 1

Answer:  The correct option is

(A) {KL}.

Step-by-step explanation: Given that Joe, Keitaro, and Luis play tennis. They put their names in a hat and choose two names without looking in order to decide who will play against each other in the first match.

We are to select the subset A that represents the complement of the event in which Joe plays in the first match.

The set of all possible outcomes (Universal set) is given by

S ={JK, KL, JL}

The event that Joe plays in the first match is given by

E = {JK, JL}

Therefore, the complement of the event E is

E' = S - E = {JK, KL, JL} - {JK, JL} = {KL}.

Thus, option (A) is CORRECT.  

Answer 2

Answer:

{KL}

Step-by-step explanation:

The order does not matter

Hope it helps!