Question

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 Type	Passenger car	Pickup Truck	SUV	Crossover	Minivan
Probability	$0.46$	$0.15$	$0.10$	$?$	$0.05$

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

(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 is$0.15$.

Step-by-step solution

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 Type	Passenger car	Pickup Truck	SUV	Crossover	Minivan
Probability	$0.46$	$0.15$	$0.10$	?	$0.05$

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 be$x$.

$0.46+0.15+0.10+x+0.05=1$

$0.76+x=1$

$x=0.24$

Probability of choosing crossover vehicle is$0.24$.

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 .

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) $$\begin{gathered} =1-(0.10+0.05) \\ =1-0.15 \\ =0.85 \end{gathered}$$

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 .

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 $0.15$