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 less than 5. event b: the number rolled is even. 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 or b\: (b) event \a and b\: (c) the complement of the event b:

Explanation:

Step1: List all possible outcomes

The sample space \(S=\{1,2,3,4,5,6\}\)

Step2: Determine outcomes for event \(A\)

Event \(A\): \(A = \{1,2,3,4\}\) (since numbers less than \(5\) are \(1,2,3,4\))

Step3: Determine outcomes for event \(B\)

Event \(B\): \(B=\{2,4,6\}\) (even numbers from \(1 - 6\))

Step4: Find \(A\) or \(B\) ( \(A\cup B\))

\(A\cup B=\{1,2,3,4,6\}\) (combine all elements in \(A\) and \(B\) without repetition)

Step5: Find \(A\) and \(B\) ( \(A\cap B\))

\(A\cap B = \{2,4\}\) (common elements in \(A\) and \(B\))

Step6: Find complement of \(B\) (\(\overline{B}\))

\(\overline{B}=\{1,3,5\}\) (elements in \(S\) not in \(B\))

Answer:

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