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 probability formula

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

Step2: Substitute values

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

Answer:

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