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 a number of less than 4
Event B: The marble selected has an even number.

Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.

Answer 1

'A or B' = {1,2,3,4,6,8}

'A and B' = {2}

The complement of A = {4,5,6,7,8)

Explanation:

Here, the sample space of possible outcomes = { 1,2,3,4,5,6,7,8}

Event A: The marble selected has a number of less than 4

So, favorable outcomes here= {1,2,3)

Event B: The marble selected has an even number.

So, favorable outcomes here= {2,4,6,8)

Total number of outcomes in Event 'A or B' = A U B = {1,2,3,4,6,8}

⇒ 'A or B' = {1,2,3,4,6,8}

Total number of outcomes in Event 'A and B' = A ∩ B = {2}

⇒ 'A and B' = {2}

Now, The complement of A = Sample Space - Element in A

= {4,5,6,7,8}

⇒The complement of A = {4,5,6,7,8)