Answer to Question #206275 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

Solution

Let C denote the probability that a vehicle entering the Cavern has Canadian licence plates

$P(C)=0.12$

Let R denote the probability that it is a camper

$P(R) = 0.28$

The probability that it is a camper with Canadian plate license is

$P(C\bigcap R)= 0.09$

I) probability that a camper entering the Lurray has Canadian license plates

$P(C/R) = \frac{P(C\bigcap R)}{P(R)}$

$\frac{0.09}{0.28} = 0.321$

ii) To find probability that a vehicle with Canadian License plates entering the Lurray Cavern is a camper

we need to find;

$P(R/C) = \frac{P(R\bigcap C)}{P(C)}$

$\frac{0.09}{0.12} = 0.75$

iii) Probability that a vehicle entering the Luray Cavern does not have Canadian plates and is not a camper, We need to find

$P(C'\bigcup R')$

$1-P(C\bigcap R)$

$1-0.09$

$=0.91$