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Chapter 5: R5.4 - Review Exercises (page 356)

What kind of vehicle? : Randomly select a new vehicle sold in the United States in a certain month. The probability distribution for the type of vehicle chosen is given here.

Vehicle TypePassenger carPickup TruckSUVCrossoverMinivan
Probability0.46
0.15
0.10
?
0.05

a. What is the probability that the vehicle is a crossover? How do you know?

b. Find the probability that vehicle is not an SUV or Minivan .

c. Given that the vehicle is not a passenger car, what is the probability that it is a pickup truck?

Short Answer

Expert verified

(a) The probability that vehicle is a crossover is 0.24.

(b) The probability vehicle is not an SUV or Minivan is 0.85.

(c) The probability vehicle is not a passenger car but a pickup car is0.15.

Step by step solution

01

Part(a) - Step 1 : Given Information

We are given different of different kind of vehicles and their probability of being chosen . We need to find the probability of crossover vehicle.

Vehicle TypePassenger carPickup TruckSUVCrossoverMinivan
Probability0.46
0.150.10 ?0.05
02

Part (a) - Step 2 : Explanation

Total probability of an event to completely occur is equal to 1.

Probability of all vehicles=1

Let probability of choosing crossover bex.

0.46+0.15+0.10+x+0.05=1

0.76+x=1

x=0.24

Probability of choosing crossover vehicle is0.24.

03

Part (b) - Step 1 : Given Information

We are given different of different kind of vehicles and their probability of being chosen . We need to find the probability that vehicle is not an SUV or Minivan .

04

Part (b) - Step 2 : Explanation

Probability of an event to completely occur is equal to 1.

Probability ( Vehicle is not an SUV or Minivan) =1-(Probability of choosing SUV +Probability of choosing Minivan).

Probability ( vehicle is not an SUV or Minivan) =1-(0.10+0.05)=1-0.15=0.85

05

Part (c) - Step 1 : Given Information

We are given different of different kind of vehicles and their probability of being chosen . We need to find that if vehicle is not a passenger car, what is the probability that it is a pickup truck .

06

Part (c) - Step 2 : Explanation

The probability if vehicle is not a passenger car, but is a pickup truck is given in the problem itself and is equal to 0.15

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