Pregunta
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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

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(a) Event “A and B”: 3, 5
(b) Event “A or B”: 1, 3, 4, 5, 6, 7
© Complement of event A: 2, 4, 6, 8

Solución

(a) The event is defined as the marble being odd, so
The event is the marble being a number from 3 to 6, so
The event " and " is the intersection of and :
(b) The event " or " is the union of and :
© The complement of event , denoted , consists of all outcomes not in . Since the total sample space is
we have

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Bonus Knowledge

Let’s break this down step by step!
(a) Event " and ":
This event involves selecting a marble that is both odd (Event A) and falls between the numbers 3 and 6 (Event B). The only numbers that satisfy both conditions are 3 and 5.
(b) Event " or ":
For this event, we’re looking for marbles that are either odd (1, 3, 5, 7) or fall in the range from 3 to 6 (3, 4, 5, 6). Combining these sets, we have 1, 3, 4, 5, 6, and 7.
© The complement of the event
The complement of Event A (marbles with odd numbers) includes all the numbers that are not odd. Therefore, the complement consists of the even numbers: 2, 4, 6, and 8.

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