Question

what is p(foreign language ∩ sport)?

Explanation:

Step1: Calculate total number of elements

Total number of elements \(=24 + 14+32=70\) (Wait, no. Wait, in probability for a Venn - diagram, if we assume the numbers in the Venn - diagram represent frequencies. The formula for \(P(A\cap B)\) is \(\frac{n(A\cap B)}{n(S)}\), where \(n(A\cap B)\) is the number of elements in the intersection and \(n(S)\) is the total number of elements. From the Venn - diagram, \(n(\text{Foreign language}\cap\text{Sport}) = 14\) and \(n(S)=24 + 14+32=70\) (Wrong. Wait, no. Wait, if we assume the numbers are \(24\) (only Foreign language), \(14\) (intersection), \(32\) (only Sport). Then \(n(S)=24 + 14+32=70\) (Wrong again. Wait, no. Wait, looking at the options, the denominators are \(50\). Maybe the total number of elements \(n(S)=24+14 + 12=50\) (assuming a mis - read of the Venn - diagram numbers. If the numbers are \(24\) (only Foreign language), \(14\) (intersection), \(12\) (only Sport))
The formula for the probability of the intersection of two events \(A\) and \(B\) (here \(A=\text{Foreign language}\), \(B = \text{Sport}\)) is \(P(A\cap B)=\frac{\text{Number of elements in }A\cap B}{\text{Total number of elements}}\)
We know that \(n(\text{Foreign language}\cap\text{Sport}) = 14\) and \(n(S)=24 + 14+12=50\)

Step2: Apply the probability formula

Using the formula \(P(A\cap B)=\frac{n(A\cap B)}{n(S)}\), substituting \(n(A\cap B) = 14\) and \(n(S)=50\), we get \(P(\text{Foreign language}\cap\text{Sport})=\frac{14}{50}\)

Answer:

\(\frac{14}{50}\)