QuestionYou spin the spinner twice.
What is the probability of landing on a 4 and then landing on a 3? 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 we get a 4 on the first spin and a 3 on the second spin? Watch out! There are two 2's on the spinner, so don't get tricked into thinking there are only four possible outcomes!

STEP 2

1. Calculate the probability of landing on 4.
2. Calculate the probability of landing on 3.
3. Calculate the probability of both events happening.

STEP 3

Alright, let's break this down!
We've got a spinner with five equally sized sections.
This is key because it means each section has an equal chance of being landed on.

STEP 4

How many 4's are on the spinner?
Just one!
So, out of the five possible outcomes, only one gives us a 4.

STEP 5

That means the probability of landing on a 4 is $\frac{1}{5}$ .
One favorable outcome divided by five total possible outcomes.
Boom!

STEP 6

Now, let's think about landing on a 3.
How many 3's are on our spinner?
Just one again!

STEP 7

Since there are five total sections, the probability of landing on a 3 is also $\frac{1}{5}$ .
See? This is starting to feel like a pattern!

STEP 8

Here's the magic!
When we want to find the probability of two independent events happening one after the other, we multiply their individual probabilities.
What does independent mean?
It means the outcome of the first spin doesn't affect the outcome of the second spin.

STEP 9

So, the probability of landing on a 4 and then landing on a 3 is: $\frac{1}{5} \cdot \frac{1}{5}$

STEP 10

Multiply the numerators (the top numbers) together: $1 \cdot 1 = 1$ .
Then, multiply the denominators (the bottom numbers) together: $5 \cdot 5 = 25$ .

STEP 11

This gives us our final probability: $\frac{1}{25}$ .
That's it!
We've cracked the code!

STEP 12

The probability of landing on a 4 and then landing on a 3 is $\frac{1}{25}$ .

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QuestionYou spin the spinner twice.
What is the probability of landing on a 4 and then landing on a 3? 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 we get a 4 on the first spin and a 3 on the second spin? Watch out! There are two 2's on the spinner, so don't get tricked into thinking there are only four possible outcomes!

STEP 2

1. Calculate the probability of landing on 4.
2. Calculate the probability of landing on 3.
3. Calculate the probability of both events happening.

STEP 3

Alright, let's break this down!
We've got a spinner with five equally sized sections.
This is key because it means each section has an equal chance of being landed on.

STEP 4

How many 4's are on the spinner?
Just one!
So, out of the five possible outcomes, only one gives us a 4.

STEP 5

That means the probability of landing on a 4 is $\frac{1}{5}$ .
One favorable outcome divided by five total possible outcomes.
Boom!

STEP 6

Now, let's think about landing on a 3.
How many 3's are on our spinner?
Just one again!

STEP 7

Since there are five total sections, the probability of landing on a 3 is also $\frac{1}{5}$ .
See? This is starting to feel like a pattern!

STEP 8

Here's the magic!
When we want to find the probability of two independent events happening one after the other, we multiply their individual probabilities.
What does independent mean?
It means the outcome of the first spin doesn't affect the outcome of the second spin.

STEP 9

So, the probability of landing on a 4 and then landing on a 3 is: $\frac{1}{5} \cdot \frac{1}{5}$

STEP 10

Multiply the numerators (the top numbers) together: $1 \cdot 1 = 1$ .
Then, multiply the denominators (the bottom numbers) together: $5 \cdot 5 = 25$ .

STEP 11

This gives us our final probability: $\frac{1}{25}$ .
That's it!
We've cracked the code!

STEP 12

The probability of landing on a 4 and then landing on a 3 is $\frac{1}{25}$ .

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QuestionYou spin the spinner twice.What is the probability of landing on a 4 and then landing on a 3? 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 we get a 4 on the first spin and a 3 on the second spin? Watch out! There are two 2's on the spinner, so don't get tricked into thinking there are only four possible outcomes!

STEP 2

1. Calculate the probability of landing on 4.2. Calculate the probability of landing on 3.3. Calculate the probability of both events happening.

STEP 3

Alright, let's **break this down**!We've got a spinner with five equally sized sections.This is **key** because it means each section has an equal chance of being landed on.

STEP 4

How many 4's are on the spinner?Just **one**!So, out of the five possible outcomes, only one gives us a 4.

STEP 5

That means the probability of landing on a 4 is 15\frac{1}{5}51​.One favorable outcome divided by five total possible outcomes.Boom!

STEP 6

Now, let's think about landing on a 3.How many 3's are on our spinner?Just **one** again!

STEP 7

Since there are five total sections, the probability of landing on a 3 is also 15\frac{1}{5}51​.See? This is starting to feel like a pattern!

STEP 8

Here's the **magic**!When we want to find the probability of two independent events happening one after the other, we **multiply** their individual probabilities.What does independent mean?It means the outcome of the first spin doesn't affect the outcome of the second spin.

STEP 9

So, the probability of landing on a 4 *and then* landing on a 3 is: 15⋅15 \frac{1}{5} \cdot \frac{1}{5} 51​⋅51​

STEP 10

Multiply the numerators (the top numbers) together: 1⋅1=11 \cdot 1 = 11⋅1=1.Then, multiply the denominators (the bottom numbers) together: 5⋅5=255 \cdot 5 = 255⋅5=25.

STEP 11

This gives us our **final probability**: 125\frac{1}{25}251​.That's it!We've cracked the code!

STEP 12

The probability of landing on a 4 and then landing on a 3 is 125\frac{1}{25}251​.

Get Studdy

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 a 4 and then landing on a 3? Simplify your answer and write it as a fraction or whole number. $\square$

1. Calculate the probability of landing on 4.
2. Calculate the probability of landing on 3.
3. Calculate the probability of both events happening.

Alright, let's break this down!
We've got a spinner with five equally sized sections.
This is key because it means each section has an equal chance of being landed on.

How many 4's are on the spinner?
Just one!
So, out of the five possible outcomes, only one gives us a 4.

That means the probability of landing on a 4 is $\frac{1}{5}$ .
One favorable outcome divided by five total possible outcomes.
Boom!

Now, let's think about landing on a 3.
How many 3's are on our spinner?
Just one again!

Since there are five total sections, the probability of landing on a 3 is also $\frac{1}{5}$ .
See? This is starting to feel like a pattern!

Here's the magic!
When we want to find the probability of two independent events happening one after the other, we multiply their individual probabilities.
What does independent mean?
It means the outcome of the first spin doesn't affect the outcome of the second spin.

So, the probability of landing on a 4 and then landing on a 3 is: $\frac{1}{5} \cdot \frac{1}{5}$

Multiply the numerators (the top numbers) together: $1 \cdot 1 = 1$ .
Then, multiply the denominators (the bottom numbers) together: $5 \cdot 5 = 25$ .

This gives us our final probability: $\frac{1}{25}$ .
That's it!
We've cracked the code!

The probability of landing on a 4 and then landing on a 3 is $\frac{1}{25}$ .