Math / Data & Statistics

QuestionYou spin the spinner twice.
What is the probability of landing on an odd number and then landing on an odd number? Simplify your answer and write it as a fraction or whole number. $\square$

Studdy Solution

STEP 1

What is this asking? If we spin this spinner two times in a row, what are the chances that both spins land on an odd number? Watch out! Don't forget that probability is about how likely something is to happen, so our answer should be between 0 and 1!

STEP 2

1. Find the probability of landing on an odd number on one spin.
2. Find the probability of landing on an odd number twice.

STEP 3

Alright, let's break this down!
We've got a spinner with three sections: 6, 7, and 8.
How many total possible outcomes are there when we spin it once?
Well, it could land on 6, 7, or 8, so there are three possible outcomes!

STEP 4

Now, how many of these outcomes are odd numbers?
Only the number 7 is odd.
So, there's only one odd number out of the three possible outcomes.

STEP 5

The probability of landing on an odd number in one spin is the number of favorable outcomes (landing on an odd number) divided by the total number of possible outcomes.
In our case, that's $\frac{\textbf{1}}{\textbf{3}}$ .
One out of three!

STEP 6

Now, we want to know the probability of landing on an odd number on two spins in a row.
Since the spins are independent events (meaning one spin doesn't affect the other), we can multiply the probabilities of each event happening.

STEP 7

We already figured out that the probability of landing on an odd number on one spin is $\frac{1}{3}$ .
So, the probability of landing on an odd number twice is: $\frac{1}{3} \cdot \frac{1}{3}$

STEP 8

Let's calculate that!
When we multiply fractions, we multiply the numerators together and the denominators together: $\frac{1 \cdot 1}{3 \cdot 3} = \frac{\textbf{1}}{\textbf{9}}$

STEP 9

So, the probability of landing on an odd number and then landing on an odd number is $\frac{1}{9}$ .

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QuestionYou spin the spinner twice.
What is the probability of landing on an odd number and then landing on an odd number? Simplify your answer and write it as a fraction or whole number. $\square$

Studdy Solution

STEP 1

What is this asking? If we spin this spinner two times in a row, what are the chances that both spins land on an odd number? Watch out! Don't forget that probability is about how likely something is to happen, so our answer should be between 0 and 1!

STEP 2

1. Find the probability of landing on an odd number on one spin.
2. Find the probability of landing on an odd number twice.

STEP 3

Alright, let's break this down!
We've got a spinner with three sections: 6, 7, and 8.
How many total possible outcomes are there when we spin it once?
Well, it could land on 6, 7, or 8, so there are three possible outcomes!

STEP 4

Now, how many of these outcomes are odd numbers?
Only the number 7 is odd.
So, there's only one odd number out of the three possible outcomes.

STEP 5

The probability of landing on an odd number in one spin is the number of favorable outcomes (landing on an odd number) divided by the total number of possible outcomes.
In our case, that's $\frac{\textbf{1}}{\textbf{3}}$ .
One out of three!

STEP 6

Now, we want to know the probability of landing on an odd number on two spins in a row.
Since the spins are independent events (meaning one spin doesn't affect the other), we can multiply the probabilities of each event happening.

STEP 7

We already figured out that the probability of landing on an odd number on one spin is $\frac{1}{3}$ .
So, the probability of landing on an odd number twice is: $\frac{1}{3} \cdot \frac{1}{3}$

STEP 8

Let's calculate that!
When we multiply fractions, we multiply the numerators together and the denominators together: $\frac{1 \cdot 1}{3 \cdot 3} = \frac{\textbf{1}}{\textbf{9}}$

STEP 9

So, the probability of landing on an odd number and then landing on an odd number is $\frac{1}{9}$ .

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QuestionYou spin the spinner twice.What is the probability of landing on an odd number and then landing on an odd number? Simplify your answer and write it as a fraction or whole number. □\square□

Studdy Solution

STEP 1

What is this asking? If we spin this spinner two times in a row, what are the chances that both spins land on an odd number? Watch out! Don't forget that probability is about how likely something is to happen, so our answer should be between 0 and 1!

STEP 2

1. Find the probability of landing on an odd number on one spin.2. Find the probability of landing on an odd number twice.

STEP 3

Alright, let's **break this down**!We've got a spinner with three sections: 6, 7, and 8.How many total possible outcomes are there when we spin it once?Well, it could land on 6, 7, or 8, so there are **three** possible outcomes!

STEP 4

Now, how many of these outcomes are *odd* numbers?Only the number **7** is odd.So, there's only **one** odd number out of the **three** possible outcomes.

STEP 5

The probability of landing on an odd number in one spin is the number of **favorable outcomes** (landing on an odd number) divided by the **total number of possible outcomes**.In our case, that's 13 \frac{\textbf{1}}{\textbf{3}} 31​.One out of three!

STEP 6

Now, we want to know the probability of landing on an odd number on *two* spins in a row.Since the spins are **independent events** (meaning one spin doesn't affect the other), we can **multiply** the probabilities of each event happening.

STEP 7

We already figured out that the probability of landing on an odd number on one spin is 13 \frac{1}{3} 31​.So, the probability of landing on an odd number *twice* is: 13⋅13 \frac{1}{3} \cdot \frac{1}{3} 31​⋅31​

STEP 8

Let's **calculate** that!When we multiply fractions, we multiply the numerators together and the denominators together: 1⋅13⋅3=19 \frac{1 \cdot 1}{3 \cdot 3} = \frac{\textbf{1}}{\textbf{9}} 3⋅31⋅1​=91​

STEP 9

So, the probability of landing on an odd number and then landing on an odd number is 19 \frac{1}{9} 91​.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionYou spin the spinner twice.
What is the probability of landing on an odd number and then landing on an odd number? Simplify your answer and write it as a fraction or whole number. $\square$

1. Find the probability of landing on an odd number on one spin.
2. Find the probability of landing on an odd number twice.

Alright, let's break this down!
We've got a spinner with three sections: 6, 7, and 8.
How many total possible outcomes are there when we spin it once?
Well, it could land on 6, 7, or 8, so there are three possible outcomes!

Now, how many of these outcomes are odd numbers?
Only the number 7 is odd.
So, there's only one odd number out of the three possible outcomes.

The probability of landing on an odd number in one spin is the number of favorable outcomes (landing on an odd number) divided by the total number of possible outcomes.
In our case, that's $\frac{\textbf{1}}{\textbf{3}}$ .
One out of three!

Now, we want to know the probability of landing on an odd number on two spins in a row.
Since the spins are independent events (meaning one spin doesn't affect the other), we can multiply the probabilities of each event happening.

We already figured out that the probability of landing on an odd number on one spin is $\frac{1}{3}$ .
So, the probability of landing on an odd number twice is: $\frac{1}{3} \cdot \frac{1}{3}$

Let's calculate that!
When we multiply fractions, we multiply the numerators together and the denominators together: $\frac{1 \cdot 1}{3 \cdot 3} = \frac{\textbf{1}}{\textbf{9}}$

So, the probability of landing on an odd number and then landing on an odd number is $\frac{1}{9}$ .