Question

question 3 of 10
this venn diagram shows the pizza topping preferences for 9 students.

let event ( a = ) the student likes pepperoni.
let event ( b = ) the student likes olives.

what is ( p(a \text{ or } b) )?

Explanation:

Step1: Count the number of students in \(A\) or \(B\)

Students in \(A\) (likes pepperoni): Joe, Kalie, Noah, Maria, Zack, Bo.
Students in \(B\) (likes olives): Maria, Zack, Bo, Julia.
Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\).
\(n(A) = 6\), \(n(B)=4\), \(n(A\cap B) = 3\). So \(n(A\cup B)=6 + 4-3=7\).

Step2: Calculate the probability

The total number of students \(N = 9\).
The probability \(P(A\cup B)=\frac{n(A\cup B)}{N}\).
Substitute \(n(A\cup B) = 7\) and \(N = 9\) into the formula, we get \(P(A\cup B)=\frac{7}{9}\).

Answer:

A. \(\frac{7}{9}\)