Question

question 18 of 25
this venn diagram shows sports played by 10 students.
let event ( a = ) the student plays basketball.
let event ( b = ) the student plays soccer.
what is ( p(a|b) )?
a. ( \frac{3}{10}=0.30 )
b. ( \frac{3}{6}=0.50 )

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{n(A\cap B)}{n(B)}\).

Step2: Identify \(n(A\cap B)\) and \(n(B)\) from the Venn - diagram

• \(n(A\cap B)\) (the number of students who play both basketball and soccer) is the number of elements in the intersection of the two sets. From the Venn - diagram, the students in the intersection are Ella, Mai, and Karl, so \(n(A\cap B) = 3\).
• \(n(B)\) (the number of students who play soccer) is the number of elements in the soccer set. The students who play soccer are Ella, Mai, Karl, Mickey, and Marcus, so \(n(B)=6\).

Step3: Calculate \(P(A|B)\)

Substitute \(n(A\cap B) = 3\) and \(n(B)=6\) into the formula \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). We get \(P(A|B)=\frac{3}{6}=0.50\).

Answer:

B. \(\frac{3}{6}=0.50\)