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

Explanation:

Step1: List the outcomes for each event

• Event \(A=\{2,4,6,8\}\) (even numbers from 1 - 8)
• Event \(B = \{4,5,6,7,8\}\) (numbers greater than 3 from 1 - 8)

Step2: Find \(A\cap B\) (Event "A and B")

The intersection of two sets \(A\) and \(B\) contains elements that are in both \(A\) and \(B\).
\(A\cap B=\{4,6,8\}\)

Step3: Find \(A\cup B\) (Event "A or B")

The union of two sets \(A\) and \(B\) contains elements that are in \(A\), in \(B\), or in both.
\(A\cup B=\{2,4,5,6,7,8\}\)

Step4: Find \(\overline{B}\) (Complement of event \(B\))

The complement of a set \(B\) contains elements that are not in \(B\) but are in the universal set \(U = \{1,2,3,4,5,6,7,8\}\)
\(\overline{B}=\{1,2,3\}\)

Answer:

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