Question

a marble is selected from a bag containing eight marbles numbered 1 to 8. the number on the marble selected will be recorded as the outcome. consider the following events. event a: the marble selected has an odd number. event b: the marble selected has a number from 3 to 6. 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: Determine outcomes for Event A

Event A: Odd numbers from 1 - 8. So outcomes: \(1, 3, 5, 7\).

Step2: Determine outcomes for Event B

Event B: Numbers from 3 - 6. So outcomes: \(3, 4, 5, 6\).

Step3: Solve (a) Event "A or B"

Combine all unique outcomes from A and B. So \(1, 3, 4, 5, 6, 7\).

Step4: Solve (b) Event "A and B"

Find common outcomes in A and B. So \(3, 5\).

Step5: Solve (c) Complement of Event B

Outcomes not in B (from 1 - 8). So \(1, 2, 7, 8\).

Answer:

(a) \(1, 3, 4, 5, 6, 7\)
(b) \(3, 5\)
(c) \(1, 2, 7, 8\)