Question

question 22 of 25 this table shows how many sophomores and juniors attended two school events. a student is selected randomly from this group. what is the probability that the student attended the volleyball game, given that the student is a sophomore? round your answer to two decimal places. a. 0.45 b. 0.36

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of this problem, if \(A\) is the event that the student attended the volleyball game and \(B\) is the event that the student is a sophomore, then \(P(A|B)=\frac{\text{Number of sophomores who attended volleyball game}}{\text{Total number of sophomores}}\).

Step2: Identify the relevant values from the table

From the table, the number of sophomores who attended the volleyball game is \(42\), and the total number of sophomores is \(77\).

Step3: Calculate the probability

Substitute the values into the formula: \(P = \frac{42}{77}\).

$$ \frac{42}{77}=\frac{6}{11}\approx0.54545\approx0.45 $$

Answer:

A. \(0.45\)