A city planner surveyed 151 residents. For each, the planner recorded whether the resident owns a car and whether the resident lives alone. The results are summarized in the table below.AloneNot aloneCar9 48No car28 66Suppose a resident from the survey is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a)What is the probability that the resident does not own a car and lives alone?(b)What is the probability that the resident does not own a car or lives alone?
Question
A city planner surveyed 151 residents. For each, the planner recorded whether the resident owns a car and whether the resident lives alone. The results are summarized in the table below.AloneNot aloneCar9 48No car28 66Suppose a resident from the survey is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a)What is the probability that the resident does not own a car and lives alone?(b)What is the probability that the resident does not own a car or lives alone?
Solution
(a) To find the probability that the resident does not own a car and lives alone, we need to divide the number of residents who do not own a car and live alone by the total number of residents surveyed.
From the table, we can see that there are 28 residents who do not own a car and live alone. The total number of residents surveyed is 151.
Therefore, the probability that the resident does not own a car and lives alone is 28/151, which is approximately 0.185.
(b) To find the probability that the resident does not own a car or lives alone, we need to add the probabilities of the resident not owning a car and the resident living alone, and then subtract the probability of the resident not owning a car and living alone (which we calculated in part (a)).
From the table, we can see that there are 28 residents who do not own a car and 9 residents who live alone. The total number of residents surveyed is 151.
Therefore, the probability that the resident does not own a car or lives alone is (28/151) + (9/151) - (28/151), which simplifies to 9/151, which is approximately 0.06.
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