contestada

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 PassCars Trucks TotalUsed537330867Did not use9046491553Total14419792420a) If one of these vehicles is selected at random, determine the probability that the vehicle is a car.b) If one of these vehicles is selected at random, determine the probability that the vehicle is a car, given that it used the toll passa) The probability that the vehicle was a car is(Round to four decimal places as needed.)

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 elect class=

Respuesta :

We are given a two-way probability table

Part a)

If one of the vehicles is selected at random, determine the probability that the vehicle is a car.

From the table, we see that the total number of cars are 1441

Also, the total number of vehicles is 2420

Then the probability of selecting a car is

[tex]P(car)=\frac{1441}{2420}=0.5955[/tex]

Therefore, the probability that the vehicle was a car is found to be 0.5955

Part b)

If one of the vehicles is selected at random, determine the probability that it used the electronic toll pass, given that it was a car.

This is a conditional probability problem.

The conditional probability is given by

[tex]P(used\: |\: car)=\frac{n(used\: and\: car)}{n(car)}[/tex]

From the table, we see that,

[tex]\begin{gathered} n(car\: and\: used)=537 \\ n(car)=1441 \end{gathered}[/tex]

So, the probability is

[tex]\begin{gathered} P(used\: |\: car)=\frac{n(used\: and\: car)}{n(car)} \\ P(used\: |\: car)=\frac{537}{1441} \\ P(used\: |\: car)=0.3727 \end{gathered}[/tex]

Therefore, the probability that it used the electronic toll pass, given that it was a car is found to be 0.3727

Otras preguntas