Question

200 students were polled about their favorite pizza toppings. 98 preferred pepperoni, 62 preferred veggie, and 40 preferred both. Find the probability that a student prefers pepperoni or veggies. Write your answer as a simplified fraction.

Answer 1

To find the probability that a student prefers either pepperoni or veggie pizza toppings, we can use the principle of inclusion-exclusion to calculate the number of students who prefer either topping.

Let:
- \( P \) be the number of students who prefer pepperoni.
- \( V \) be the number of students who prefer veggie.
- \( P \cap V \) be the number of students who prefer both pepperoni and veggie.

From the problem, we have:
- \( P = 98 \)
- \( V = 62 \)
- \( P \cap V = 40 \)

Using the principle of inclusion-exclusion, the number of students who prefer either pepperoni or veggie (or both) is given by:

\[
|P \cup V| = |P| + |V| - |P \cap V|
\]

Substituting in the values:

\[
|P \cup V| = 98 + 62 - 40 = 120
\]

So, 120 students prefer either pepperoni, veggie, or both.

Now, to find the probability that a randomly selected student prefers either topping, we divide the number of students who prefer either topping by the total number of students polled:

\[
P(\text{pepperoni or veggie}) = \frac{|P \cup V|}{\text{Total students}} = \frac{120}{200}
\]

Simplifying this fraction:

\[
\frac{120}{200} = \frac{12}{20} = \frac{3}{5}
\]

Therefore, the probability that a student prefers either pepperoni or veggies is

\[
\boxed{\frac{3}{5}}.
\]