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 regular hiking.
Probability is defined as the study of likeliness of an event to happen.
It has a range of 0 to 1 , where 0 means uncertain while 1 indicates certainty.
In the given question the table shows the results of a survey of 200 randomly selected people about where they live and whether they hike regularly.
Assuming A is the people who do not regulary hike
B are the people who live near a lake.
P(A given B ) = P(A and B)/P(B)
When two events are Independent.
if P( A given B) = P(A)
From the data given in the question , we can determine
P(A) = 100/200 = 0.5
P(B) = 48/200 = 0.24
P(A and B) = 24/200 = 0.12
P(A given B) = (24/200)/(48/200) = 24/48 = 0.5 = P(A)
As both the probabilities are equal , Therefore A and B are independent.
So now the statement can be completed as
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 regular hiking.
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