To determine which equation can be used to calculate the probability of a visitor riding either the largest or the smallest roller coaster, we need to apply the basic principle of probability for the union of two events.
We denote the following probabilities:
- [tex]\( P(\text{largest}) \)[/tex] as the probability of riding the largest roller coaster, which is 0.30 (or 30%),
- [tex]\( P(\text{smallest}) \)[/tex] as the probability of riding the smallest roller coaster, which is 0.20 (or 20%),
- [tex]\( P(\text{both}) \)[/tex] as the probability of riding both roller coasters, which is 0.15 (or 15%).
The formula for the probability of the union of two events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] (in this case, riding the largest or the smallest roller coaster) is given by:
[tex]\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\][/tex]
Substituting our specific probabilities into this formula:
[tex]\[
P(\text{largest or smallest}) = P(\text{largest}) + P(\text{smallest}) - P(\text{both})
\][/tex]
Using the given values:
[tex]\[
P(\text{largest or smallest}) = 0.30 + 0.20 - 0.15
\][/tex]
Thus, the correct equation to calculate the probability of a visitor riding the largest or the smallest roller coaster is:
[tex]\[
P(\text{largest or smallest}) = 0.30 + 0.20 - 0.15
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{P(\text{largest or smallest}) = 0.30 + 0.20 - 0.15}
\][/tex]
