Question

a student is randomly selected from this table. what is the probability that they are a boy, given that they are a junior? students on a team freshman sophomore junior senior boy 7 9 7 5 girl 5 5 4 2 p(boy | junior) = p(b|a) = \frac{p(a and b)}{p(a)}

Explanation:

Step1: Find the number of juniors

The number of junior boys is \(7\) and the number of junior girls is \(4\). So the total number of juniors is \(7 + 4=11\).

Step2: Apply the conditional - probability formula

The formula for conditional probability \(P(\text{Boy}|\text{Junior})=\frac{\text{Number of boy juniors}}{\text{Total number of juniors}}\). Substituting the values, we get \(P(\text{Boy}|\text{Junior})=\frac{7}{11}\).

Answer:

\(\frac{7}{11}\)