Let's solve this step by step:

Problem Breakdown:

We are given a contingency table summarizing the students in a class based on whether they have a brother or a sister. The goal is to find the probability that a randomly chosen student has a sister.

Data Table Recap:

Step 1: Identify the Total Number of Students

The total number of students in the class is: $30$

Step 2: Identify the Number of Students Who Have a Sister

From the first row of the table, the number of students who have a sister is: $2 + 6 = 8$

Step 3: Calculate the Probability

The probability that a randomly chosen student has a sister is given by: $P(\text{Has a sister}) = \frac{\text{Number of students who have a sister}}{\text{Total number of students}}$

Substitute the values: $P(\text{Has a sister}) = \frac{8}{30}$

Simplify: $P(\text{Has a sister}) = \frac{4}{15}$

Final Answer:

The probability that a randomly chosen student has a sister is: $\boxed{\frac{4}{15}}$

Would you like me to explain any step in more detail? Here are 5 questions related to this problem:

1. How is the probability calculated for "does not have a sister"?
2. How do we calculate joint probabilities using a contingency table?
3. What is the probability that a student has both a sister and a brother?
4. How can this be extended to conditional probabilities (e.g., has a sister given they have a brother)?
5. How would the probabilities change if the table entries were different?

Tip:

Always verify totals in contingency tables by summing rows and columns—they must match the grand total!