Question

the table shows the number of cars and trucks that used a certain toll road on a particular day. the number of cars and trucks that used, and did not use, an electronic toll pass on that same day was also recorded.
toll pass
used
did not use
total
cars
537
975
1512
trucks
313
666
979
total
850
1641
2491
a) if one of these vehicles is selected at random, determine the probability that the vehicle was a car.
b) if one of these vehicles is selected at random, determine the probability that the vehicle was a car, given that the vehicle did not use a toll pass.
the probability that the vehicle was a car is 0.6070.
(round to four decimal places as needed.)
the probability that the vehicle was a car, given that the vehicle did not use a toll pass, is
(round to four decimal places as needed.)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of this problem, for part b, \(A\) is "the vehicle was a car" and \(B\) is "the vehicle did not use a toll pass". So \(P(A|B)=\frac{\text{Number of cars that did not use toll pass}}{\text{Total number of vehicles that did not use toll pass}}\)

Step2: Identify the relevant values from the table

From the table, the number of cars that did not use a toll pass is \(975\), and the total number of vehicles that did not use a toll pass is \(1641\)

Step3: Calculate the probability

\(P=\frac{975}{1641}\approx 0.5941\)

Answer:

\(0.5941\)