Question

the last 56 boat rentals at a boat rental company were 34 sunfish, 8 kayaks, and 14 rowboats. use this information to complete parts (a) through (c).
a) determine the empirical probability that the next boat rental is a sunfish.
b) determine the empirical probability that the next boat rental is a kayak.
c) determine the empirical probability that the next boat rental is a rowboat.
a) p(sunfish) = (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for empirical probability

Empirical probability \(P(E)=\frac{\text{Number of times event }E\text{ occurred}}{\text{Total number of trials}}\)

Step2: Identify values for part (a)

For sunfish, the number of times sunfish was rented \(n = 34\), and the total number of boat - rentals \(N=56\)

Step3: Calculate \(P(\text{sunfish})\)

\(P(\text{sunfish})=\frac{34}{56}=\frac{17}{28}\)

Step4: Identify values for part (b)

For kayaks, the number of times kayaks was rented \(n = 8\), and the total number of boat - rentals \(N = 56\)

Step5: Calculate \(P(\text{kayak})\)

\(P(\text{kayak})=\frac{8}{56}=\frac{1}{7}\)

Step6: Identify values for part (c)

For rowboats, the number of times rowboats was rented \(n=14\), and the total number of boat - rentals \(N = 56\)

Step7: Calculate \(P(\text{rowboat})\)

\(P(\text{rowboat})=\frac{14}{56}=\frac{1}{4}\)

Answer:

a) \(P(\text{sunfish})=\frac{17}{28}\)
b) \(P(\text{kayak})=\frac{1}{7}\)
c) \(P(\text{rowboat})=\frac{1}{4}\)