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: $A \cup B = B$

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Quizplus · Accepted Answer

Event A is the sum of the numbers on the dice is 3, which can only happen when one die shows 1 and the other shows 2. Event B is at least one of the dice shows a 2, which can happen when one die shows 2 and the other shows any number, or when both dice show 2. Therefore, A is a subset of B, and A ∪ B = B.

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

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