Answer to Question #206495 in Statistics and Probability for Attari

Question

The probability that a vehicle entering the Luray Caverns has Canadian 

license plates is 0.12; the probability that it is a camper is 0.28; and the 

probability that it is a camper with Canadian license plates is 0.09. What is 

the probability that 

(i) A camper entering the Luray Caverns has Canadian license Plates.

(ii) A vehicle with Canadian license plates entering the Luray Caverns is a 

camper. 

(iii) A vehicle entering the Luray Caverns does not have Canadian plates or 

is not a camper.

Answer 1

Probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.12

Probability that a vehicle entering the Luray Caverns is a camper is 0.28.

Probability that it is a camper with Canadian license plates is 0.09

Let A be an event which denotes that a vehicle entering the Luray Caverns has Canadian license plates. Then,

P(A)=0.12

Let A' be an event which denotes that a vehicle entering the Luray Caverns does not have Canadian license plates.

Let B be an event which denotes that a vehicle entering the Luray Caverns is a Camper. Then,

P(B)=0.28

Let B' be an event which denotes that a vehicle entering the Luray Caverns is not a Camper

Probability that it is a camper with Canadian license plates can be written as: P(A and B) = 0.09

i) To find the probability that a camper entering the Luray Caverns has Canadian license plates:

Conditional probability formula:

$P(A | B)= \frac{P(A \;and \;B)}{P(B)} \\ = \frac{0.09}{0.28} \\ =0.32143$

Therefore, probability that a camper entering the Luray Caverns has Canadian license plates is 0.32

ii) To find the probability that a vehicle with Canadian license plates entering the Luray Caverns is a camper:

$P(B | A)= \frac{P(B \;and \;A)}{P(A)} \\ = \frac{P(A \;and\; B)}{P(A)} \\ = \frac{0.09}{0.12} \\ =0.75$

Therefore, probability that a vehicle with Canadian license plates entering the Luray Caverns is a camper is 0.75

iii) To find the probability that a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper:

Required probability is: P(A' OR B')

P(A' OR B')=1−P(A and B)

=1−0.09

=0.91

Therefore, probability that a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper is 0.91