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 greater than 4 . Event B : The number rolled is odd. 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 " A and B ": (b) Event "A or B" : (c) The complement of the event B :

Answer 1

Event 'A and B' has the single outcome {5}. Event 'A or B' includes all outcomes that are either greater than 4 or odd, resulting in {1, 3, 5, 6}. The complement of event B includes all even number outcomes, which are {2, 4, 6}.

Step-by-step explanation:

When rolling a number cube with faces labeled from 1 to 6, we consider different events based on the outcome of the roll. Event A is that the number rolled is greater than 4, which has the outcomes {5, 6}. Event B is that the number rolled is odd, which has the outcomes {1, 3, 5}.

• (a) Event "A and B" means the outcome must satisfy both conditions of being greater than 4 and being odd. The only outcome that fits both criteria is 5.
• (b) Event "A or B" includes all outcomes that satisfy either or both conditions. The outcomes are {1, 3, 5, 6} since 1 and 3 are odd, and 5 and 6 are greater than 4.
• (c) The complement of the event B includes all the outcomes that are not odd, which are the even numbers. Therefore, the outcomes are {2, 4, 6}.