Math / Data & Statistics

QuestionConditional Probability from a Table Score: $2 / 5$ Penalty: 1 off
Question Show Examples
In a class of students, the following data table summarizes how many students have a brother a sister. What is the probability that a student has a brother given that they have a sister? \begin{tabular}{|c|c|c|} \hline & Has a brother & Does not have a brother \\ \hline Has a sister & 3 & 20 \\ \hline Does not have a sister & 2 & 4 \\ \hline \end{tabular}
Answer Attempt 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

What is this asking? Out of all the students who have a sister, what are the chances they also have a brother? Watch out! Don't mix up the total number of students with the number of students who have a sister!

STEP 2

1. Find the total number of students with a sister.
2. Find the number of students with both a sister and a brother.
3. Calculate the conditional probability.

STEP 3

Let's look at the row "Has a sister".
We see $\text{3}$ students have both a sister and a brother, and $\text{20}$ students have a sister but no brother.

STEP 4

To find the total number of students with a sister, we add these two groups together: $3 + 20 = 23$ .
So, there are $\textbf{23}$ students with a sister.

STEP 5

This is given directly in the table!
Look at the cell where the "Has a sister" row and the "Has a brother" column meet.
It tells us there are $\textbf{3}$ such students.

STEP 6

Remember, the conditional probability is the number of students with both a sister and a brother, divided by the total number of students with a sister.

STEP 7

We already found these numbers!
The number of students with both is $\text{3}$ , and the total number of students with a sister is $\text{23}$ .

STEP 8

So, the probability is $\frac{3}{23}$ .

STEP 9

The probability that a student has a brother given that they have a sister is $\frac{3}{23}$ .

Was this helpful?

Studdy Solution

STEP 1

What is this asking? Out of all the students who have a sister, what are the chances they also have a brother? Watch out! Don't mix up the total number of students with the number of students who have a sister!

STEP 2

1. Find the total number of students with a sister.
2. Find the number of students with both a sister and a brother.
3. Calculate the conditional probability.

STEP 3

Let's look at the row "Has a sister".
We see $\text{3}$ students have both a sister and a brother, and $\text{20}$ students have a sister but no brother.

STEP 4

To find the total number of students with a sister, we add these two groups together: $3 + 20 = 23$ .
So, there are $\textbf{23}$ students with a sister.

STEP 5

This is given directly in the table!
Look at the cell where the "Has a sister" row and the "Has a brother" column meet.
It tells us there are $\textbf{3}$ such students.

STEP 6

Remember, the conditional probability is the number of students with both a sister and a brother, divided by the total number of students with a sister.

STEP 7

We already found these numbers!
The number of students with both is $\text{3}$ , and the total number of students with a sister is $\text{23}$ .

STEP 8

So, the probability is $\frac{3}{23}$ .

STEP 9

The probability that a student has a brother given that they have a sister is $\frac{3}{23}$ .

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.

Studdy Solution

STEP 1

What is this asking? Out of all the students who have a sister, what are the chances they *also* have a brother? Watch out! Don't mix up the total number of students with the number of students who have a sister!

STEP 2

1. Find the total number of students with a sister.2. Find the number of students with *both* a sister and a brother.3. Calculate the conditional probability.

STEP 3

Let's look at the row "Has a sister".We see 3\text{3}3 students have *both* a sister and a brother, and 20\text{20}20 students have a sister but *no* brother.

STEP 4

To find the **total number of students with a sister**, we add these two groups together: 3+20=233 + 20 = 233+20=23.So, there are 23\textbf{23}23 students with a sister.

STEP 5

This is given directly in the table!Look at the cell where the "Has a sister" row and the "Has a brother" column meet.It tells us there are 3\textbf{3}3 such students.

STEP 6

Remember, the **conditional probability** is the number of students with *both* a sister and a brother, divided by the *total* number of students with a sister.

STEP 7

We already found these numbers!The number of students with both is 3\text{3}3, and the total number of students with a sister is 23\text{23}23.

STEP 8

So, the probability is 323\frac{3}{23}233​.

STEP 9

The probability that a student has a brother given that they have a sister is 323\frac{3}{23}233​.

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.

What is this asking? Out of all the students who have a sister, what are the chances they also have a brother? Watch out! Don't mix up the total number of students with the number of students who have a sister!

1. Find the total number of students with a sister.
2. Find the number of students with both a sister and a brother.
3. Calculate the conditional probability.

Let's look at the row "Has a sister".
We see $\text{3}$ students have both a sister and a brother, and $\text{20}$ students have a sister but no brother.

To find the total number of students with a sister, we add these two groups together: $3 + 20 = 23$ .
So, there are $\textbf{23}$ students with a sister.

This is given directly in the table!
Look at the cell where the "Has a sister" row and the "Has a brother" column meet.
It tells us there are $\textbf{3}$ such students.

Remember, the conditional probability is the number of students with both a sister and a brother, divided by the total number of students with a sister.

We already found these numbers!
The number of students with both is $\text{3}$ , and the total number of students with a sister is $\text{23}$ .

So, the probability is $\frac{3}{23}$ .

The probability that a student has a brother given that they have a sister is $\frac{3}{23}$ .