To determine the probability that a randomly chosen student does not have a brother, we first need to calculate the total number of students and the number of students who do not have a brother.
From the table:
- Students who have a brother and have a sister: 2
- Students who do not have a brother and have a sister: 6
- Students who have a brother and do not have a sister: 5
- Students who do not have a brother and do not have a sister: 8
Let's summarize the data:
- Students who have a brother: \( 2 + 5 = 7 \)
- Students who do not have a brother: \( 6 + 8 = 14 \)
Now we can calculate the total number of students:
\[ \text{Total Students} = (Has : brother : and : has : sister) + (Does : not : have : brother : and : has : sister) + (Has : brother : and : does : not : have : sister) + (Does : not : have : brother : and : does : not : have : sister) \]
Substituting the values:
\[ \text{Total Students} = 2 + 6 + 5 + 8 = 21 \]
Next, we focus on the number of students who do not have a brother, which we calculated earlier as 14.
Now we can find the probability that a randomly chosen student does not have a brother:
\[ P(\text{Does not have a brother}) = \frac{\text{Number of students who do not have a brother}}{\text{Total number of students}} = \frac{14}{21} \]
To simplify this fraction:
\[ \frac{14}{21} = \frac{2}{3} \]
Thus, the probability that a randomly chosen student does not have a brother is
\[ \boxed{\frac{2}{3}}. \]