Question

Of the people who fished at Clearwater Park today, 64 had a fishing license, and 16 did not. Of the people who fished at Mountain View Park today, 63 had a license, and 7 did not. (No one fished at both parks.) Suppose that one fisher from each park is chosen at random. What is the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license? Do not round your answer. (If necessary, consult a list of formulas.)

Answer 1

To calculate the probability that a randomly chosen fisher from Clearwater Park did not have a license while one from Mountain View Park did, you multiply the individual probabilities of these independent events from each park.

Step-by-step explanation:

To find the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license, we use the multiplication rule for independent events. The events at the two parks are independent because no one fished at both parks.

First, calculate the probability for Clearwater Park: Total fishers at Clearwater = 64 (with license) + 16 (without license) = 80 fishers. The probability that a fisher at Clearwater did not have a license is P(Clearwater without license) = 16/80.

Next, calculate the probability for Mountain View Park: Total fishers at Mountain View = 63 (with license) + 7 (without license) = 70 fishers. The probability that a fisher at Mountain View had a license is P(Mountain View with license) = 63/70.

Now, multiply both probabilities to get the combined probability: P(Clearwater without license AND Mountain View with license) = (16/80) × (63/70).

Step-by-step calculation:

1. Calculate the individual probabilities for each event.

2. Apply the multiplication rule for independent events by multiplying the individual probabilities.

3. Simplify the answer to get the combined probability.

The final result from the multiplication will be the answer to the question.