This table shows how many sophomores and juniors attended two school events. A student is selected randomly from this group.

\begin{tabular}{|c|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 the student attended the jazz concert, given that the student is a sophomore?



Answer :

Certainly! Let's solve this probability question step-by-step.

Firstly, we need to find the probability that a randomly selected sophomore attended the jazz band concert.

1. Identify the total number of sophomores: From the table, we can see that the total number of sophomores is 77.

2. Identify the number of sophomores who attended the jazz band concert: According to the table, 35 sophomores attended the jazz band concert.

3. Calculate the probability: The probability is calculated by dividing the number of sophomores who attended the jazz band concert by the total number of sophomores.

So, the probability [tex]\( P(\text{sophomore attends jazz concert}) \)[/tex] is:

[tex]\[ P(\text{sophomore attends jazz concert}) = \frac{\text{Number of sophomores who attended the jazz concert}}{\text{Total number of sophomores}} \][/tex]

[tex]\[ P(\text{sophomore attends jazz concert}) = \frac{35}{77} \][/tex]

After performing the division:

[tex]\[ P(\text{sophomore attends jazz concert}) \approx 0.45454545454545453 \][/tex]

Therefore, the probability that a randomly selected sophomore attended the jazz band concert is approximately [tex]\( 0.4545 \)[/tex] or [tex]\( 45.45\% \)[/tex].