EXAMPLE 4 Assigning Probabilities to Means of Transportation

How do people in the United States get to work? Table 8.1 shows the results of an American Community Survey by the U.S. Census Bureau.

Table 8.1: Table 8.1 Survey Results from the American Community Survey, 2013
Means of Travel Frequency
Drive alone 107,460,210
Carpool 13,675,867
Public transportation (excluding taxis) 7,053,456
Walk 3,969,058
Work at home 6,143,943
Other 2,560,426
Total 140,862,960

Because this is a U.S. Census Bureau survey, we can assume that the sample fairly represents the workers in the United States. Given the large sample size, the sample proportions should be good estimates of the probabilities for each category of transportation. Table 8.2 turns the data from the survey into a probability model for means of transportation to work. Notice that the probabilities are all between 0 and 1 (Rule 1) and that the sum of the probabilities is 1 (Rule 2).

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Table 8.2: Table 8.2 Probability Model for Means of Transportation to Work
Means of Travel Proportion/Probability
Drive alone 0.763
Carpool 0.097
Public transportation
(excluding taxis)		 0.050
Walk 0.028
Work at home 0.044
Other 0.018
Sum 1

Based on the probabilities in Table 8.2, a randomly selected worker is almost 8 times more likely to drive alone to work than to carpool and more than 15 times more likely I to drive alone than to use pubic transportation.