Question

Approximately $86.5\%$of Americans commute to work by car, truck, or van. Out of that group, $84.6\%$drive alone and$15.4\%$drive in a carpool. Approximately $3.9\%$walk to work and approximately$5.3\%$take public transportation.

a. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.

b. Assuming that the walkers walk alone, what percent of all commuters travel alone to work?

c. Suppose that$1,000$ workers are randomly selected. How many would you expect to travel alone to work?

d. Suppose that $1,000$ workers are randomly selected. How many would you expect to drive in a carpool?

Short answer

a. The table representation is :

b. The probability of all commuters travelling alone to work is $0.77080r77.08\%$

c. The number of workers that would travel alone to work is $771.$

d. The number of workers that would drive in carpool is $133$.

Step-by-step solution

Content Introduction

We are given:

$86.5\%$commute through various modes of transport

$84.6\%$drive alone

$15.4\%$drive in carpool

$3.9\%$walk to work

$5.3\%$take public transport

Explanation (part a)

Probability of an event is defined as:$P=\frac{Numberoffavorableoutcomes}{totalnumberofpossibleoutcomes}$

The table representation is as follow:

Explanation (Part b)

The probability of an event $E$is calculated as:

$P=\frac{Numberoffavorableoutcomes}{totalnumberofpossibleoutcomes}$

From the table represented in step 2, we have alone travellers $=0.7318,$and walking travellers total is$0.0390$

The probability of all commuters that travel alone to work is as follows:

$$\begin{gathered} 0.7318+0.0390 \\ =0.7708 \\ =77.08\% \end{gathered}$$

Explanation (Part c)

The probability of an event $E$is,

$P=\frac{Numberoffavorableoutcomes}{totalnumberofpossibleoutcomes}$

From the table we have

The probability of all commuters travelling alone to work $=0.7708$

Total number of workers $1000$

Thus a number of workers who would want to travel alone to work is calculated as:

$$\begin{gathered} 0.7708\times 1000 \\ =770.8 \\ =771 \end{gathered}$$

Explanation (Part d)

Probability of an event $E$is

$P=\frac{Numberoffavorableoutcomes}{totalnumberofpossibleoutcomes}$

The probability of all commuters driving in carpool is$0.1332$

Total number of workers $1000$

Thus, number of workers who would travel in carpool is

$$\begin{gathered} 0.1332\times 1000 \\ =133.2 \\ =133 \end{gathered}$$