A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The sum of the numbers on the dice is 3}
B: {At least one of the dice shows a 2}
True or False: $$A \cup B = B$$

Question

Quizplus · Accepted Answer

Event A is a subset of Event B because the only way to get a sum of 3 is by rolling a 1 and a 2, which satisfies the condition of Event B (at least one die shows a 2). Therefore, the union of A and B is just B, as A does not add any new outcomes to B.

A Pair of Fair Dice Is Tossed A∪B=BA \cup B = BA∪B=B

A Pair of Fair Dice Is Tossed $A \cup B = B$