Question

question
for a certain class, the following data table compares how many students have a brother or a sister. what is
the probability that a randomly chosen student from the class does not have a sister?

has a sister\tdoes not have a sister
has a brother\t5\t2
does not have a brother\t13\t3

answer
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Explanation:

Step1: Calculate total students

First, find the total number of students by adding all the values in the table. The values are 5 (has sister, has brother), 2 (does not have sister, has brother), 13 (has sister, does not have brother), and 3 (does not have sister, does not have brother). So total = \(5 + 2 + 13 + 3 = 23\)? Wait, no, wait. Wait, the question is about the probability that a randomly chosen student does not have a sister. So first, find the number of students who do not have a sister. The "Does not have a sister" column has values 2 (has brother) and 3 (does not have brother). So number of students without sister is \(2 + 3 = 5\)? Wait, no, wait the table:

Rows: Has a brother, Does not have a brother

Columns: Has a sister, Does not have a sister

So:

- Has a sister and has a brother: 5

- Does not have a sister and has a brother: 2

- Has a sister and does not have a brother: 13

- Does not have a sister and does not have a brother: 3

So total number of students: \(5 + 2 + 13 + 3 = 23\)? Wait, no, wait the question is "does not have a sister". So the number of students who do not have a sister is the sum of the "Does not have a sister" column: \(2 + 3 = 5\)? Wait, no, 2 (has brother, no sister) + 3 (no brother, no sister) = 5. Wait, total students: sum all cells: 5 + 2 + 13 + 3 = 23? Wait, no, 5 + 2 is 7, 13 + 3 is 16, 7 + 16 is 23. Wait, but the number of students without sister is 2 + 3 = 5? Wait, no, that can't be. Wait, maybe I misread. Wait, the columns are "Has a sister" and "Does not have a sister". Rows are "Has a brother" and "Does not have a brother". So:

- Has sister, Has brother: 5

- Has sister, Does not have brother: 13

- Does not have sister, Has brother: 2

- Does not have sister, Does not have brother: 3

So total students: 5 + 13 + 2 + 3 = 23.

Number of students who do not have a sister: 2 (has brother, no sister) + 3 (no brother, no sister) = 5. Wait, no, 2 + 3 = 5? Wait, 2 + 3 is 5. Then the probability is (number of students without sister) / total students = \( \frac{2 + 3}{5 + 2 + 13 + 3} = \frac{5}{23} \)? Wait, no, wait the question is "does not have a sister". Wait, no, wait the table:

Wait, the columns are "Has a sister" and "Does not have a sister". So the "Does not have a sister" column has two entries: 2 (has brother) and 3 (does not have brother). So total without sister: 2 + 3 = 5. Total students: 5 (has sister, has brother) + 13 (has sister, no brother) + 2 (no sister, has brother) + 3 (no sister, no brother) = 5 + 13 is 18, 2 + 3 is 5, total 23. So probability is \( \frac{5}{23} \)? Wait, no, wait maybe I made a mistake. Wait, the question is "the probability that a randomly chosen student from the class does not have a sister". So number of students without sister: 2 (has brother, no sister) + 3 (no brother, no sister) = 5. Total students: 5 + 13 + 2 + 3 = 23. So probability is \( \frac{5}{23} \approx 0.217 \)? Wait, but let's check again.

Wait, no, wait the table:

- Has a sister: 5 (has brother) + 13 (does not have brother) = 18

- Does not have a sister: 2 (has brother) + 3 (does not have brother) = 5

Total students: 18 + 5 = 23. So yes, number of students without sister is 5, total is 23. So probability is \( \frac{5}{23} \). Wait, but let me confirm the table again. The user's table:

Row 1: Has a brother

- Has a sister: 5

- Does not have a sister: 2

Row 2: Does not have a brother

- Has a sister: 13

- Does not have a sister: 3

So total without sister: 2 + 3 = 5. Total students: 5 + 2 + 13 + 3 = 23. So probability is \( \frac{5}{23} \).

Step1: Find number of students without sister

Number of students who do not have a sister: sum of "Does not have a sister" column: \(2 + 3 = 5\)

Step2: Find total number of students

Total number of students: sum all cells: \(5 + 2 + 13 + 3 = 23\)

Step3: Calculate probability

Probability = (Number of students without sister) / (Total number of students) = \( \frac{5}{23} \approx 0.217 \) or as a fraction \( \frac{5}{23} \)

Wait, but let me check again. Wait, maybe the table is:

Wait, the first column is "Has a brother" and "Does not have a brother", rows. Columns: "Has a sister" and "Does not have a sister".

So:

- Has a brother:

- Has a sister: 5

- Does not have a sister: 2

- Does not have a brother:

- Has a sister: 13

- Does not have a sister: 3

So total students: 5 + 2 + 13 + 3 = 23.

Number of students without sister: 2 (has brother, no sister) + 3 (no brother, no sister) = 5.

Thus, probability is \( \frac{5}{23} \).

Answer:

\(\boxed{\dfrac{5}{23}}\)