Question

probability determining outcomes for unions, intersections, and complements of... 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: Define sets for A and B

Event A = {2, 4, 6} (even - numbered outcomes), Event B = {4, 5, 6} (outcomes greater than 3)

Step2: Find "A and B" (intersection)

The intersection of A and B, A ∩ B, consists of elements that are in both A and B. So A ∩ B={4, 6}

Step3: Find "A or B" (union)

The union of A and B, A ∪ B, consists of all elements that are in A or B (or both). So A ∪ B = {2, 4, 5, 6}

Step4: Find the complement of B

The sample - space S = {1, 2, 3, 4, 5, 6}. The complement of B, B', consists of elements in S that are not in B. So B'={1, 2, 3}

Answer:

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