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

A ∪ B is the event that either the sum of the numbers on the dice is 3 or at least one of the dice shows a 2. B is the event that at least one of the dice shows a 2. Since the sum of the numbers on the dice can only be 3 if one of the dice shows a 2, 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 $A \cup B = B$