Question

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

Explanation:

Step1: Find the number of girls who are sophomores

From the table, the number of girls who are sophomores is \(5\).

Step2: Find the total number of girls

The total number of girls is \(5 + 5+4 + 2=16\).

Step3: Calculate the conditional probability

Using the formula \(P(B|A)=\frac{P(A\cap B)}{P(A)}\), here \(A\) is the event of being a girl and \(B\) is the event of being a sophomore. So \(P(\text{Sophomore}|\text{Girl})=\frac{\text{Number of girl - sophomores}}{\text{Total number of girls}}\)
\(P(\text{Sophomore}|\text{Girl})=\frac{5}{16}\)

Answer:

\(\frac{5}{16}\)