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 even number. event b: the marble selected has a number 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 or b\: (b) event \a and b\: (c) the complement of the event a:

Explanation:

Step1: Find outcomes for event A and event B

Event A (even number): \( \{2,4,6,8\} \)
Event B (number > 3): \( \{4,5,6,7,8\} \)

Step2: Find "A or B" (union)

Union of two sets is all elements in either set.
\( A\cup B=\{2,4,5,6,7,8\} \)

Step3: Find "A and B" (intersection)

Intersection is elements common to both sets.
\( A\cap B = \{4,6,8\} \)

Step4: Find complement of A

Complement of A (\(\overline{A}\)) is elements not in A.
\(\overline{A}=\{1,3,5,7\}\)

Answer:

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