# Definition of a multiple within a probability problem.

• tempneff
In summary, the conversation discusses a test problem in Probability class where the person missed points because they counted 0 as a multiple of 3. The person approached their professor with this concern and was told that 0 is not a multiple of 3. They then provide their solution to the problem and ask for advice on how to approach their professor again. The output of the conversation is a summary of the problem and their solution, as well as a question about seeking advice from a respected mathematician.
tempneff
Below is a test problem I recently had in Probability class. I missed points on this problem (event B) because I counted 0 as a multiple of 3. But...0 is a multiple of 3 right?

I approached my professor with this concern and he told me that 0 is definately not a multiple of 3...
If I am right, can I have some advice on how to approach him again, or if I should at all. I lost 10% of the test grade which I could not afford..

Here's what I turned in...

1. Homework Statement

An urn contains 10 identical balls numbered 0,1,...9. A random experiment involves selecting a ball from the urn and noting the number of the ball. The events A,B,C are defined as follows:
A "number of the ball selected is odd."
B "number of the ball selected is a multiple of 3,"
C "number of the ball selected is less than 5,"

Find ##P(A),P(B),P(C),P(A\cup B), \text{ and } P(A\cup B \cup C).##

## Homework Equations

Let ##\mathbb{Z}## denote the integers.
Say ##d## divides ##m##, equivalently, that ##m## is a multiple of ##d##, if there exists an integer ##q## such that ##m = qd##.

Let ##m=q=0 \text{ and } d=3##

then ##m=qd \Longrightarrow 0=0\times 3##

##\therefore 0 \text{ is a multiple of }3##

## The Attempt at a Solution

[/B]
$S= \{0,1,2,3,4,5,6,7,8,9\}$

##A= \{1,3,5,7,9\} \hspace{20pt} B= \{ 0,3,6,9\} \hspace{20pt}C=\{0,1,2,3,4\}##

##P(A)=\frac{5}{10}\hspace{20pt}P(B)=\frac{4}{10}\hspace{20pt}P(C)=\frac{5}{10}##

##P(A \cup B) =\frac{7}{10} \hspace{20pt} P(A \cup B \cup C) = \frac{9}{10}##

tempneff said:
Below is a test problem I recently had in Probability class. I missed points on this problem (event B) because I counted 0 as a multiple of 3. But...0 is a multiple of 3 right?

I approached my professor with this concern and he told me that 0 is definately not a multiple of 3...
If I am right, can I have some advice on how to approach him again, or if I should at all. I lost 10% of the test grade which I could not afford..

Here's what I turned in...

1. Homework Statement

An urn contains 10 identical balls numbered 0,1,...9. A random experiment involves selecting a ball from the urn and noting the number of the ball. The events A,B,C are defined as follows:
A "number of the ball selected is odd."
B "number of the ball selected is a multiple of 3,"
C "number of the ball selected is less than 5,"

Find ##P(A),P(B),P(C),P(A\cup B), \text{ and } P(A\cup B \cup C).##

...

I'm not sure how to approach him regarding this. Do you know a mathematician that he respects? (He must not be one himself.)

## 1. What is a multiple within a probability problem?

A multiple within a probability problem refers to a situation where an event can occur multiple times in a given scenario. This is different from a single outcome, where only one specific result can occur.

## 2. How is a multiple determined in a probability problem?

To determine a multiple in a probability problem, you need to identify the total number of possible outcomes and the number of outcomes that meet the desired criteria. The multiple is then calculated by dividing the number of desired outcomes by the total number of possible outcomes.

## 3. What is the significance of multiples in probability problems?

The concept of multiples is important in probability because it allows us to calculate the likelihood of an event occurring multiple times within a given scenario. This can be useful in predicting future outcomes and making informed decisions.

## 4. Can multiples be greater than 1 in a probability problem?

Yes, multiples can be greater than 1 in a probability problem. This indicates that the desired outcome is more likely to occur multiple times than not occur at all.

## 5. How does understanding multiples help in solving probability problems?

Understanding multiples can help in solving probability problems by providing a way to calculate the likelihood of an event occurring multiple times. This can help in making predictions and determining the most probable outcomes in a given scenario.

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