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Chapter 4: Problem 124

A car rental agency currently has 44 cars available, 28 of which have a GPS navigation system. One of the 44 cars is selected at random. Find the probability that this car a. has a GPS navigation system b. does not have a GPS navigation system

Short Answer

Expert verified
The probability that a randomly selected car has a GPS system is 0.6364 and the probability that it doesn't have a GPS system is 0.3636.

Step by step solution

01

Understand the problem and gather data

We need to find out the probability of selecting a car with a GPS system and one that doesn't. For this we need the total number of cars, which is 44 and the number of cars with GPS, which is 28.
02

Calculate the probability of a car having a GPS system

To calculate a probability, we divide the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is picking a car with a GPS system. So, we will divide the number of cars with GPS (28) by the total number of cars (44). So the probability \(P(GPS)\) is \(\frac{28}{44} = 0.6364\) when rounded to four decimal places.
03

Calculate the probability of a car not having a GPS system

Similarly, to calculate the probability of a car not having a GPS system, we need to divide the number of cars without GPS by the total number of cars. As we know there are 44 cars in total and 28 have a GPS, so 44 - 28 = 16 cars do not have a GPS. Therefore, the probability is \(P(NoGPS)\) is \(\frac{16}{44} = 0.3636\) when rounded to four decimal places.

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