R5.4 - Review Exercises What kind of vehicle? : 聽Random... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

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 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

Expert verified

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

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

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) $= 1 - (0.10 + 0.05) = 1 - 0.15 = 0.85$

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 .