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 brother	does not have a brother
does not have a sister	2	3

Explanation:

Step1: Calculate total number of students

First, we find the total number of students by adding up all the values in the table. The values are 5 (has sister and brother), 13 (has sister, no brother), 2 (no sister, has brother), and 3 (no sister, no brother). So total students = \(5 + 13 + 2 + 3\).
\(5 + 13 + 2 + 3 = 23\)

Step2: Calculate number of students without a sister

Next, we find the number of students who do not have a sister. This is the sum of the values in the "Does not have a sister" row, which is \(2 + 3\).
\(2 + 3 = 5\)

Step3: Calculate the probability

The probability that a randomly chosen student does not have a sister is the number of students without a sister divided by the total number of students. So probability = \(\frac{\text{Number of students without a sister}}{\text{Total number of students}}=\frac{5}{23}\) (Wait, no, wait. Wait, 2 + 3 is 5? Wait, no, 2 (has brother, no sister) + 3 (no brother, no sister) is 5? Wait, no, 2 + 3 is 5? Wait, let's recalculate total students: 5 (has sister, has brother) + 13 (has sister, no brother) = 18 (has sister). Then 2 (no sister, has brother) + 3 (no sister, no brother) = 5 (no sister). So total students is 18 + 5 = 23. Then number of students without a sister is 5? Wait, no, 2 + 3 is 5? Wait, 2 + 3 is 5? Yes. So probability is 5/23? Wait, no, wait, 2 + 3 is 5? Wait, 2 (has brother, no sister) and 3 (no brother, no sister) so total no sister is 2 + 3 = 5. Total students is 5 + 13 + 2 + 3 = 23. So probability is 5/23? Wait, no, wait, maybe I made a mistake. Wait, 5 (has sister, has brother) + 13 (has sister, no brother) = 18. 2 (no sister, has brother) + 3 (no sister, no brother) = 5. 18 + 5 = 23. So number of students without a sister is 5. So probability is 5/23? Wait, no, wait, 2 + 3 is 5? Wait, 2 + 3 is 5. So yes. So the probability is 5/23? Wait, no, wait, maybe I miscalculated. Wait, 5 (has sister, has brother) + 13 (has sister, no brother) = 18. 2 (no sister, has brother) + 3 (no sister, no brother) = 5. 18 + 5 = 23. So number of students without a sister is 5. So probability is 5/23. Wait, but let's check again. The table:

• Has a sister: 5 (has brother) + 13 (no brother) = 18
• Does not have a sister: 2 (has brother) + 3 (no brother) = 5

Total students: 18 + 5 = 23.

So the number of students who do not have a sister is 5, total students is 23. So probability is 5/23? Wait, no, wait, 2 + 3 is 5? Wait, 2 + 3 is 5. So yes. So the probability is 5/23. Wait, but maybe I made a mistake. Wait, 2 (no sister, has brother) and 3 (no sister, no brother) so total no sister is 2 + 3 = 5. Total students is 5 + 13 + 2 + 3 = 23. So probability is 5/23. Yes.

Answer:

\(\frac{5}{23}\)