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 The number rolled is even.
Event The number rolled is less than 4 .
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 or
(b) Event and
© The complement of the event

Ask by Ortiz Ortega. in the United States

Mar 16,2025

Question

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 The number rolled is even.
Event The number rolled is less than 4 .
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 or
(b) Event and
© The complement of the event

Ask by Ortiz Ortega. in the United States

Mar 16,2025

UpStudy AI · Accepted Answer

$$ A $$ (even numbers) is $$\{2,4,6\}$$.

$$ B $$ (numbers less than 4) is $$\{1,2,3\}$$.

The complement of $$ A $$ is 
$$
{}^{n}A = \{1,3,5\}.
$$

(a) $$ {}^{n}A $$ or $$ B^{*} $$ means the union of $${}^{n}A$$ with $$B$$. Thus, we have:
$$
{}^{n}A \cup B = \{1,3,5\} \cup \{1,2,3\} = \{1,2,3,5\}.
$$

(b) $$ {}^{n}A $$ and $$ B^{*} $$ means the intersection of $${}^{n}A$$ with $$B$$. Thus, we have:
$$
{}^{n}A \cap B = \{1,3,5\} \cap \{1,2,3\} = \{1,3\}.
$$

(c) The complement of the event $$ A $$ is already given by:
$$
{}^{n}A = \{1,3,5\}.
$$
(a) Event $$ {}^{n}A $$ or $$ B^{*} $$ includes outcomes 1, 2, 3, and 5. (b) Event $$ {}^{n}A $$ and $$ B^{*} $$ includes outcomes 1 and 3. (c) The complement of event $$ A $$ includes outcomes 1, 3, and 5.

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