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(largest or smallest) = 0.30 - 0.20 p(largest or smallest) = 0.30 + 0.15 - 0.20 p(largest or smallest) = 0.30 + 0.20 - 0.15 p(largest or smallest) = 0.30 + 0.20

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
Let \(A\) be the event of riding the largest roller - coaster (\(P(A) = 0.30\)), \(B\) be the event of riding the smallest roller - coaster (\(P(B)=0.20\)), and \(P(A\cap B) = 0.15\).

Step2: Substitute the values into the formula

Substitute \(P(A)=0.30\), \(P(B) = 0.20\), and \(P(A\cap B)=0.15\) into \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
We get \(P(A\cup B)=0.30 + 0.20-0.15\).

Answer:

\(P(\text{largest or smallest})=0.30 + 0.20-0.15\) (the third option)