Question

what is p(foreign language | sport)?

Explanation:

Step1: Calculate the total number of people in Sport

Add the number of people in the Sport circle (including the overlap).
$$14 + 10=24$$

Step2: Calculate the number of people in both Foreign language and Sport

The overlap part is \(14\).

Step3: Use the conditional - probability formula \(P(A|B)=\frac{n(A\cap B)}{n(B)}\)

Here \(A\) is Foreign language and \(B\) is Sport. So \(P(\text{Foreign language}|\text{Sport})=\frac{14}{14 + 10}\)
$$=\frac{14}{24}=\frac{7}{12}$$

Answer:

\(\frac{7}{12}\)