This table shows how many sophomores and juniors attended two school events.

\begin{tabular}{|r|c|c|c|}
\hline
& \begin{tabular}{c}
Jazz band \\
concert
\end{tabular}
& Volleyball game
& Total \\
\hline
Sophomore
& 35
& 42
& 77 \\
\hline
Junior
& 36
& 24
& 60 \\
\hline
Total
& 71
& 66
& 137 \\
\hline
\end{tabular}

What is the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game?

Round your answer to two decimal places.

A. 0.56
B. 0.48
C. 0.26
D. 0.31



Answer :

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