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 \a and b\: {} (b) event \a or b\: {} (c) the complement of the event b: {}

Explanation:

Step1: Determine outcomes for Event A

Event A: Number rolled is even. So outcomes are 2, 4, 6.

Step2: Determine outcomes for Event B

Event B: Number rolled is greater than 3. So outcomes are 4, 5, 6.

Step3: Find "A and B" (Intersection)

Outcomes common to both A and B: 4, 6.

Step4: Find "A or B" (Union)

Outcomes in A or B: Combine A and B, remove duplicates. So 2, 4, 5, 6.

Step5: Find complement of B

Complement of B: Outcomes not in B (i.e., ≤3). So 1, 2, 3.

Answer:

(a) 4, 6
(b) 2, 4, 5, 6
(c) 1, 2, 3