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Chapter 4: Problem 134

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 navigation system is \( \frac{7}{11} \) and the probability that it does not have a GPS navigation system is \( \frac{4}{11} \).

Step by step solution

01

Calculate total number of outcomes

The problem states that there are 44 cars available at the rental agency. Therefore, the total number of outcomes in this case is 44.
02

Calculate probability the car has a GPS navigation system

It's stated that 28 out of 44 cars have a GPS navigation system. The probability is given by the number of ways an event can occur divided by the total number of outcomes. Hence, the probability that the car has a GPS navigation system is 28 divided by 44, or \( \frac{28}{44} \). Reducing this fraction gives \( \frac{7}{11} \).
03

Calculate probability the car does not have a GPS navigation system

We know that 28 cars have a GPS and total cars are 44. So, the cars without GPS can be found by subtracting the cars with GPS from total cars. This results in \( 44 - 28 = 16 \). Therefore, the probability that a car does not have a GPS is \( \frac{16}{44} \), which simplifies to \( \frac{4}{11} \).

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