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ALEKS Probability Answers: Two Independent Fisher Selections

The two selections are independent: 48/80 of Clearwater fishers have licenses and 45/90 of Mountain View fishers do not, giving an exact probability of 3/10.

Question

Of the people who fished at Clearwater Park today, 48 had a fishing license, and 32 did not. Of the people who fished at Mountain View Park today, 45 had a license, and 45 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 had a license and the fisher chosen from Mountain View did not have a license?Do not round your answer. (If necessary, consult a list of formulas.)

Answer

Let AA be the event that the selected Clearwater fisher has a license, and let BB be the event that the selected Mountain View fisher does not.

1. Clearwater probability

There are 48+32=8048+32=80 Clearwater fishers, so

P(A)=4880=35.P(A)=\frac{48}{80}=\frac{3}{5}.

2. Mountain View probability

There are 45+45=9045+45=90 Mountain View fishers, so

P(B)=4590=12.P(B)=\frac{45}{90}=\frac{1}{2}.

3. Probability that both events occur

One person is selected from each separate park population. Under the random-selection conditions in the prompt, the two events are independent, so multiply their probabilities:

P(A∩B)=P(A)P(B)=35×12=310.P(A\cap B)=P(A)P(B) =\frac{3}{5}\times\frac{1}{2} =\boxed{\frac{3}{10}}.

The exact probability is 310\frac{3}{10}; no rounding is needed.

Evidence boundary

This calculation uses only the 48, 32, 45, and 45 counts in the locked question version and assumes an equally likely random selection from each park's listed population. It does not use values from other algorithmically generated ALEKS variants.

Sources

These references support the concepts and methods used in the explanation above.

ALEKS Probability Answer: Independent Events | Verla