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 The marble selected has an odd number.
Event : The marble selected has a number from 3 to 6 .
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 " and ": {[}
(b) Event " or ":
© The complement of the event

Ask by Luna Wells. in the United States

Mar 16,2025

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 The marble selected has an odd number.
Event : The marble selected has a number from 3 to 6 .
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 " and ": {[}
(b) Event " or ":
© The complement of the event

Ask by Luna Wells. in the United States

Mar 16,2025

UpStudy AI · Accepted Answer

(a) The event $$ A $$ is defined as the marble being odd, so  
$$
A = \{1, 3, 5, 7\}.
$$  
The event $$ B $$ is the marble being a number from 3 to 6, so  
$$
B = \{3, 4, 5, 6\}.
$$  
The event " $$ A $$ and $$ B $$ " is the intersection of $$ A $$ and $$ B $$:  
$$
A \cap B = \{3, 5\}.
$$

(b) The event " $$ A $$ or $$ B $$ " is the union of $$ A $$ and $$ B $$:  
$$
A \cup B = \{1, 3, 5, 7\} \cup \{3, 4, 5, 6\} = \{1, 3, 4, 5, 6, 7\}.
$$

(c) The complement of event $$ A $$, denoted $$ A^c $$, consists of all outcomes not in $$ A $$. Since the total sample space is  
$$
S = \{1, 2, 3, 4, 5, 6, 7, 8\},
$$  
we have  
$$
A^c = S \setminus A = \{2, 4, 6, 8\}.
$$
(a) Event "A and B": 3, 5 (b) Event "A or B": 1, 3, 4, 5, 6, 7 (c) Complement of event A: 2, 4, 6, 8

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