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].
