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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 greater than 4.
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:

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 class=

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Answer:

a)  A ∪ B = {2, 4, 5, 6}

b)  A ∩ B = {6}

c)  [tex]\sf B^c[/tex] = {1, 3, 5}

Step-by-step explanation:

Set notation is used in math to list numbers, objects or outcomes.

It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.

The listing method of set notation simply lists the numbers in the set.

The three dots "..." means it is infinite (goes on forever).

Given:

  • A number cube with faces labeled 1 to 6.

Therefore the set of all possible outcomes is {1, 2, 3, 4, 5, 6}.

Event A

The number rolled is greater than 4.

Therefore, the set of outcomes for event A is {5, 6}.

Event B

The number rolled is even.

Therefore, the set of outcomes for event B is {2, 4, 6}.

Part (a)
Event "A or B" means the outcomes in A or B or both.

⇒ A ∪ B = {2, 4, 5, 6}

Part (b)

Event "A and B" means the outcomes in both A and B.

⇒  A ∩ B = {6}

Part (c)

The complement of event B means everything that is not in B.

[tex]\sf \implies B^c =[/tex] {1, 3, 5}

Learn more about set notation here:

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