Question

a city planner surveyed 169 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.

	alone	not alone
no car	22	90

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.

(a) what is the probability that the resident does not live alone?

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

Explanation:

Part (a)

Step 1: Find total residents not alone

Residents not alone: Car (18) + No car (90) = 18 + 90 = 108.

Step 2: Calculate probability

Total residents = 169. Probability = $\frac{108}{169} \approx 0.64$.

Step 1: Define events

Let \( A \): does not own a car, \( B \): does not live alone.

Step 2: Find counts

• \( n(A) \): No car (22 + 90) = 112.
• \( n(B) \): Not alone (18 + 90) = 108.
• \( n(A \cap B) \): No car and not alone = 90.

Step 3: Apply inclusion - exclusion

\( n(A \cup B)=n(A)+n(B)-n(A \cap B)=112 + 108 - 90 = 130 \).

Step 4: Calculate probability

Probability = $\frac{130}{169} \approx 0.77$.

Answer:

0.64

Part (b)