QuestionAssume that a fair die is rolled. The sample space is $\{1,2,3,4,5,6\}$ , and all the outcomes are equally likely. Find $P(5)$ . Express your answer in exact form. $P(5)=$ $\square$ $\square$

Studdy Solution

STEP 1

What is this asking? Hey there!
This problem is asking us to find the probability of rolling a 5 on a fair die. Watch out! Don't forget that each side of a fair die has an equal chance of landing face up!

STEP 2

1. Define the sample space
2. Identify the favorable outcome
3. Calculate the probability

STEP 3

Alright, let's start by understanding what a sample space is.
It's just a fancy way of saying "all possible outcomes." For a fair six-sided die, the sample space is $\{1, 2, 3, 4, 5, 6\}$ .
Each number represents one side of the die.
So, there are 6 possible outcomes.

STEP 4

Now, let's figure out what we're looking for.
We want the probability of rolling a 5.
So, our favorable outcome is the number 5 itself.
There's only 1 favorable outcome here.

STEP 5

Here's the fun part!
To find the probability, we use the formula:
$P(\text{favorable outcome}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

STEP 6

Plugging in our numbers, we get:
$P(5) = \frac{1}{6}$ This tells us that the probability of rolling a 5 is $\frac{1}{6}$ .

STEP 7

The probability of rolling a 5 on a fair die is $\frac{1}{6}$ .

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QuestionAssume that a fair die is rolled. The sample space is $\{1,2,3,4,5,6\}$ , and all the outcomes are equally likely. Find $P(5)$ . Express your answer in exact form. $P(5)=$ $\square$ $\square$

Studdy Solution

STEP 1

What is this asking? Hey there!
This problem is asking us to find the probability of rolling a 5 on a fair die. Watch out! Don't forget that each side of a fair die has an equal chance of landing face up!

STEP 2

1. Define the sample space
2. Identify the favorable outcome
3. Calculate the probability

STEP 3

Alright, let's start by understanding what a sample space is.
It's just a fancy way of saying "all possible outcomes." For a fair six-sided die, the sample space is $\{1, 2, 3, 4, 5, 6\}$ .
Each number represents one side of the die.
So, there are 6 possible outcomes.

STEP 4

Now, let's figure out what we're looking for.
We want the probability of rolling a 5.
So, our favorable outcome is the number 5 itself.
There's only 1 favorable outcome here.

STEP 5

Here's the fun part!
To find the probability, we use the formula:
$P(\text{favorable outcome}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

STEP 6

Plugging in our numbers, we get:
$P(5) = \frac{1}{6}$ This tells us that the probability of rolling a 5 is $\frac{1}{6}$ .

STEP 7

The probability of rolling a 5 on a fair die is $\frac{1}{6}$ .

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QuestionAssume that a fair die is rolled. The sample space is {1,2,3,4,5,6}\{1,2,3,4,5,6\}{1,2,3,4,5,6}, and all the outcomes are equally likely. Find P(5)P(5)P(5). Express your answer in exact form. P(5)=P(5)=P(5)= □\square□ □\square□

Studdy Solution

STEP 1

What is this asking? Hey there!This problem is asking us to find the probability of rolling a **5** on a fair die. Watch out! Don't forget that each side of a fair die has an equal chance of landing face up!

STEP 2

1. Define the sample space2. Identify the favorable outcome3. Calculate the probability

STEP 3

Alright, let's start by understanding what a sample space is.It's just a fancy way of saying "all possible outcomes." For a fair six-sided die, the sample space is {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}{1,2,3,4,5,6}.Each number represents one side of the die.So, there are **6 possible outcomes**.

STEP 4

Now, let's figure out what we're looking for.We want the probability of rolling a **5**.So, our favorable outcome is the number **5** itself.There's only **1 favorable outcome** here.

STEP 5

STEP 6

Plugging in our numbers, we get:P(5)=16P(5) = \frac{1}{6}P(5)=61​This tells us that the probability of rolling a **5** is 16\frac{1}{6}61​.

STEP 7

The probability of rolling a **5** on a fair die is 16\frac{1}{6}61​.

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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.

QuestionAssume that a fair die is rolled. The sample space is $\{1,2,3,4,5,6\}$ , and all the outcomes are equally likely. Find $P(5)$ . Express your answer in exact form. $P(5)=$ $\square$ $\square$

What is this asking? Hey there!
This problem is asking us to find the probability of rolling a 5 on a fair die. Watch out! Don't forget that each side of a fair die has an equal chance of landing face up!

1. Define the sample space
2. Identify the favorable outcome
3. Calculate the probability

Alright, let's start by understanding what a sample space is.
It's just a fancy way of saying "all possible outcomes." For a fair six-sided die, the sample space is $\{1, 2, 3, 4, 5, 6\}$ .
Each number represents one side of the die.
So, there are 6 possible outcomes.

Now, let's figure out what we're looking for.
We want the probability of rolling a 5.
So, our favorable outcome is the number 5 itself.
There's only 1 favorable outcome here.

Plugging in our numbers, we get:
$P(5) = \frac{1}{6}$ This tells us that the probability of rolling a 5 is $\frac{1}{6}$ .

The probability of rolling a 5 on a fair die is $\frac{1}{6}$ .