Question

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

Explanation:

Step1: Find the number of senior girls

From the table, the number of senior girls is \(2\).

Step2: Find the total number of seniors

The number of senior boys is \(5\) and senior girls is \(2\). So total number of seniors \(=5 + 2=7\).

Step3: Calculate the conditional probability

Using the formula \(P(\text{Girl}|\text{Senior})=\frac{\text{Number of senior girls}}{\text{Total number of seniors}}\). Substitute the values: \(P(\text{Girl}|\text{Senior})=\frac{2}{7}\).

Answer:

\(\frac{2}{7}\)