Question

an amusement park reports that the probability of a visitor riding its largest roller coaster is 30 percent, the probability of a visitor riding its smallest roller coaster is 20 percent, and the probability of a visitor riding both roller coasters is 15 percent. which equation can be used to calculate the probability of a visitor riding the largest or the smallest roller coaster? ○ ( p(\text{largest or smallest}) = 0.30 - 0.20 ) ○ ( p(\text{largest or smallest}) = 0.30 + 0.15 - 0.20 ) ○ ( p(\text{largest or smallest}) = 0.30 + 0.20 - 0.15 ) ○ ( p(\text{largest or smallest}) = 0.30 + 0.20 )

Explanation:

To find the probability of a visitor riding the largest or the smallest roller coaster, we use the principle of inclusion - exclusion for probabilities. The formula for \( P(A \cup B) \) (the probability of event \( A \) or event \( B \) occurring) is \( P(A \cup B)=P(A)+P(B)-P(A \cap B) \), where \( A \) is the event of riding the largest roller coaster, \( B \) is the event of riding the smallest roller coaster, and \( A\cap B \) is the event of riding both. Here, \( P(A) = 0.30 \), \( P(B)=0.20 \), and \( P(A\cap B) = 0.15 \). So the formula should be \( P(\text{largest or smallest})=0.30 + 0.20- 0.15 \).

Answer:

\( P(\text{largest or smallest}) = 0.30 + 0.20 - 0.15 \) (the option corresponding to this formula)