To determine the probability that a student chosen randomly from the class has a sister, we need to follow several steps:
1. Count the total number of students who have a sister.
According to the table:
- The number of students who have both a brother and a sister is 2.
- The number of students who do not have a brother but have a sister is 6.
Therefore, the total number of students who have a sister is:
[tex]\[
2 + 6 = 8
\][/tex]
2. Count the total number of students in the class.
Based on the table:
- The number of students who have both a brother and a sister is 2.
- The number of students who do not have a brother but have a sister is 6.
- The number of students who have a brother but no sister is 15.
- The number of students who have neither a brother nor a sister is 7.
Therefore, the total number of students in the class is:
[tex]\[
2 + 6 + 15 + 7 = 30
\][/tex]
3. Calculate the probability that a randomly chosen student has a sister.
The probability [tex]\( P \)[/tex] that a student chosen randomly has a sister is given by the ratio of students with a sister to the total number of students in the class:
[tex]\[
P(\text{student has a sister}) = \frac{\text{Number of students with a sister}}{\text{Total number of students}}
\][/tex]
Plugging in the numbers:
[tex]\[
P(\text{student has a sister}) = \frac{8}{30} = 0.26666666666666666
\][/tex]
Therefore, the probability that a student chosen randomly from the class has a sister is approximately [tex]\( 0.267 \)[/tex] or [tex]\( 26.67\% \)[/tex].
