Question

(a) 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
1) A camper entering the Luray Caverns has Canadian license Plates.
(1) A vehicle with Canadian license plates entering the Luray Caverns is a
camper.
(ii) A vehicle entering the Luray Caverns does not have Canadian plates or
is not a camper.​

Answer 1

p(Canadian license plates)= 0.12

p(camper)= 0.28

p( camper with Canadian license plates)= 0.09  

(a) P(camper with Canadian license plates) = .12  

(b) P(a vehicle with Canadian license plates is a camper)

P(A|B) = P(A and B)/P(B)

P(Camper| Canadian Plates) = .09/.12 = .75  

(c) P( vehicle A:does not have Canadian plates 0r B: is not a camper)

P(A 0r B) = P(A) + P(B) - P(A and B) = .88 + .72 - .81 = .80

Answer 2

Given :   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;  

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

To Find : What is the probability that

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

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

camper.

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

is not a camper.​

Solution:

probability that

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

= 0.12,

probability that

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

camper.

=  camper with Canadian license plates /  Canadian license plates

= 0.09/ 0.12

= 9/12

= 3/4

= 0.75

probability that

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

is not a camper.​  1  -  P (  Canadian plates or camper)

P (  Canadian plates or camper) = 0.12 + 0.28  - 0.09  =  0.31

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

is not a camper.​  1  -  P (  Canadian plates or camper)

= 1 - 0.31

= 0.69

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