Question

2Drive to exercise : The two-way table summarizes the responses of 120 people to a survey in which they were asked, “Do you exercise for at least 30 minutes four or more times per week?” and “What kind of vehicle do you drive?”

Exercise	Sedan	SUV	Truck
Yes	$25$	$15$	$12$
No	$20$	$24$	$24$

Suppose one person from this sample is randomly selected.

a. Find the probability that the person drives an SUV.

b. Find the probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week.

c. Find the probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week.

Short answer

(a) Probability that the person drives an SUV is $0.325$.

(b)The probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week is $0.6$.

(c)The probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week is $0.33$.

Step-by-step solution

Part (a) - Step 1 : Given Information

We are given three different vehicles and if a person exercises or not . We need to find if the person drives an SUV .

Exercise	Sedan	SUV	Truck
Yes	$25$	$15$	$12$
No	$20$	$24$	$24$

Part (a) - Step 2 : Explanation

We need to find the total and divide favorable outcome by total outcomes in order to achieve the probability .

Exercise	Sedan	SUV	Truck	Total
Yes	$25$	$15$	$12$	$52$
No	$20$	$24$	$24$	$68$
Total	$45$	$39$	$36$	$120$

So, probability (person drives an SUV ) $=\frac{39}{120}$

$=0.325$

Part (b) - Step 1 : Given Information 

We are given three different vehicles and if a person exercises or not . We need to find the probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week.

Part (b) - Step 2 : Explanation

We need to add probability of both the cases .

Probability (person drives a sedan or exercises for at least 30 minutes four or more times per week)$=$Probability (person drives a sedan) $+$Probability (sedan in total ) $-$Probability (yes in exercise)

Required probability$$\begin{gathered} =\frac{45}{120}+\frac{52}{120}-\frac{25}{120} \\ =\frac{72}{120} \\ =0.6 \end{gathered}$$

Part (c) - Step 1 : Given Information 

We are given different vehicles and if a person exercises or not. We need to find the probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week .

Part (c) - Step 2 : Explanation 

Required Probability$=$$$\begin{gathered} \frac{25}{120}+\frac{15}{120} \\ =\frac{40}{120} \\ =0.33 \end{gathered}$$