To determine the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game, let's follow these steps:
1. Identify the total number of students:
According to the table, the total number of students is 137.
2. Identify the number of sophomores who attended the volleyball game:
The table shows that 42 sophomores attended the volleyball game.
3. Calculate the probability:
The probability that a randomly chosen person is a sophomore and attended the volleyball game is given by the ratio of the number of sophomores who attended the volleyball game to the total number of students.
So, the probability [tex]\( P \)[/tex] is calculated as:
[tex]\[
P = \frac{\text{Number of sophomores who attended the volleyball game}}{\text{Total number of students}}
\][/tex]
Substituting the known values:
[tex]\[
P = \frac{42}{137}
\][/tex]
4. Round the probability to two decimal places:
Performing the division gives us approximately 0.3066. When we round this value to two decimal places, we get 0.31.
Therefore, the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game is:
[tex]\[
\boxed{0.31}
\][/tex]
The correct answer is:
D. 0.31
