Question

a city planner surveyed 153 residents. for each, the planner recorded whether the resident owns a car and whether the resident lives alone. the results summarized in the table below.

	alone	not alone
no car	19	96

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

Explanation:

Step1: Find total number of residents

The total number of residents surveyed is 153.

Step2: Calculate probability for part (a)

The number of residents who do not own a car is \(19 + 96=115\). The probability \(P(\text{no car})\) is the number of residents without a car divided by the total number of residents. So \(P(\text{no car})=\frac{115}{153}\approx 0.75\).

Step3: Calculate number of residents for part (b)

The number of residents who live alone is \(21 + 19 = 40\). Let \(A\) be the event that a resident does not own a car and \(B\) be the event that a resident lives alone. The number of residents in \(A\cup B\) is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, \(n(A) = 115\), \(n(B)=40\) and \(n(A\cap B)=19\). So \(n(A\cup B)=115 + 40- 19=136\).

Step4: Calculate probability for part (b)

The probability \(P(A\cup B)\) is \(\frac{n(A\cup B)}{153}=\frac{136}{153}\approx 0.89\).

Answer:

(a) \(0.75\)
(b) \(0.89\)