Problem

The balle 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 abo recorded \begin{tabular}{|c|c|c|r|} \hline Ioll Pass & Cars & Trucks & Total \\ \hline Used & 502 & 349 & 851 \\ Oid not use & 944 & 650 & 1594 \\ \hline Total & 1446 & 999 & 2445 \\ \hline \end{tabular} a) II one of these vehides is selected at random determine the probability that the vehicle used a tol pass b) If one of these vehides is selected at random, determine the probabilty that the vehicle used a toll pass given that the vehicle was a car The probatilify that the tandomly selected vehicle used a toll pass is 0.348 (Round to four decimal places as needed) The probabliny that the vehicle used a loll puss, given that the vehicle is a car, is $\square$ (Round to bur decimal places as needed)

Solution

Step 1 :Define the total number of vehicles as 2445, the total number of cars as 1446, and the number of cars that used a toll pass as 502.

Step 2 :Calculate the probability of both events A and B occurring, denoted as P(A ∩ B), which is the number of cars that used a toll pass divided by the total number of vehicles. The calculation is \(\frac{502}{2445} = 0.20531697341513291\).

Step 3 :Calculate the probability of event B, denoted as P(B), which is the total number of cars divided by the total number of vehicles. The calculation is \(\frac{1446}{2445} = 0.5914110429447853\).

Step 4 :Calculate the conditional probability of event A given event B, denoted as P(A|B), using the formula P(A|B) = P(A ∩ B) / P(B). The calculation is \(\frac{0.20531697341513291}{0.5914110429447853} = 0.34716459197787\).

Step 5 :Round the result to four decimal places to get the final answer. The probability that the vehicle used a toll pass, given that the vehicle is a car, is \(\boxed{0.3472}\).

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Source: https://solvelyapp.com/problems/GCKYqCYIBM/

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