Question

select the correct answer from each drop - down menu.
the table shows the results of a survey of 200 randomly selected people about where they live and whether they hike regularly.

	lives in a city	lives near mountains	lives near a lake	total
does not hike	56	20	24	100
total	84	68	48	200

complete the given statement.
not regularly hiking and living near a lake are events because the probability of not regularly hiking given that a person lives near a lake is to the probabilit | independent
dependent |

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Explanation:

Step1: Define independent events

Two events \(A\) (does not hike) and \(B\) (lives near a lake) are independent if \(P(A|B) = P(A)\).

Step2: Calculate \(P(A|B)\)

\(P(A|B)=\frac{\text{People who don't hike and live near lake}}{\text{Total people near lake}}=\frac{24}{48}=0.5\)

Step3: Calculate \(P(A)\)

\(P(A)=\frac{\text{Total people who don't hike}}{\text{Total surveyed}}=\frac{100}{200}=0.5\)

Step4: Compare probabilities

Since \(P(A|B)=P(A)=0.5\), the events are independent.

Answer:

Not regularly hiking and living near a lake are independent events because the probability of not regularly hiking given that a person lives near a lake is equal to the probability of not regularly hiking (for all surveyed people).