Question

a city planner surveyed 171 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.

	car	no car
not alone	51	71

suppose 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 does not live alone?
(b) what is the probability that the resident does not own a car or does not live alone?

Explanation:

Step1: Find total residents

Total residents = 9 + 40 + 51 + 71 = 171.

Step2: Solve part (a)

Residents with no car and not alone: 71.
Probability = $\frac{71}{171} \approx 0.4152 \approx 0.42$.

Step3: Solve part (b)

Residents with no car: 40 + 71 = 111.
Residents not alone: 51 + 71 = 122.
Residents with no car or not alone: 111 + 122 - 71 = 162.
Probability = $\frac{162}{171} \approx 0.9474 \approx 0.95$.

Answer:

(a) $\approx 0.42$
(b) $\approx 0.95$