To solve this problem, we need to use the principle of inclusion and exclusion for probabilities. This principle helps us find the probability of either of two events happening when there's an overlap between the two events.
Let's define the events:
- [tex]\( P(A) \)[/tex]: Probability of a visitor riding the largest roller coaster.
- [tex]\( P(B) \)[/tex]: Probability of a visitor riding the smallest roller coaster.
- [tex]\( P(A \cap B) \)[/tex]: Probability of a visitor riding both the largest and the smallest roller coasters.
We are given:
- [tex]\( P(A) = 0.30 \)[/tex]
- [tex]\( P(B) = 0.20 \)[/tex]
- [tex]\( P(A \cap B) = 0.15 \)[/tex]
The probability of a visitor riding either the largest or the smallest roller coaster can be found using the following formula:
[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]
We plug in the given values:
[tex]\[ P(A \cup B) = 0.30 + 0.20 - 0.15 \][/tex]
Now, we need to evaluate the right-hand side:
[tex]\[ P(A \cup B) = 0.30 + 0.20 - 0.15 = 0.35 \][/tex]
Thus, the equation that can be used to calculate the probability of a visitor riding either the largest or the smallest roller coaster is:
[tex]\[ P(\text{largest or smallest}) = 0.30 + 0.20 - 0.15 \][/tex]
Therefore, the correct equation from the given list is:
[tex]\[ P(\text{largest or smallest}) = 0.30 + 0.20 - 0.15 \][/tex]
