A number cube with faces labeled 1 to 6 is rolled once.The number rolled will be recorded as the outcome.Consider the following events.Event A: The number rolled is even.Event B: The number rolled is greater than 3.Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.(a) Event"AandB":(b) Event"AorB":(c) The complement of the event B:
Question
A number cube with faces labeled 1 to 6 is rolled once.The number rolled will be recorded as the outcome.Consider the following events.Event A: The number rolled is even.Event B: The number rolled is greater than 3.Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.(a) Event"AandB":(b) Event"AorB":(c) The complement of the event B:
Solution
(a) Event "A and B": This event represents the intersection of events A and B, meaning the outcomes that satisfy both conditions. The even numbers on the cube are 2, 4, and 6. The numbers greater than 3 are 4, 5, and 6. Therefore, the outcomes that satisfy both conditions are 4 and 6.
(b) Event "A or B": This event represents the union of events A and B, meaning the outcomes that satisfy either condition. The even numbers on the cube are 2, 4, and 6. The numbers greater than 3 are 4, 5, and 6. Therefore, the outcomes that satisfy either condition are 2, 4, 5, and 6.
(c) The complement of the event B: The complement of an event represents all outcomes that do not satisfy the condition of the event. The numbers on the cube that are greater than 3 are 4, 5, and 6. Therefore, the outcomes that do not satisfy this condition (i.e., the numbers that are not greater than 3) are 1, 2, and 3.
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