The probability that a vehicle entering the Luray Caverns has Canadian

TokNeekCepTdh

TokNeekCepTdh

Answered question

2021-11-20

The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.19; the probability that it is a camper is 0.38; and the probability that it is a camper with Canadian license plates is 0.13. What is the probability that
(a) a camper entering the Luray Caverns has Canadian license plates?
(b) a vehicle with Canadian license plates entering the Luray Caverns is not a camper?
(c) a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper?

Answer & Explanation

Symbee

Symbee

Beginner2021-11-21Added 17 answers

Step 1
Let the event that a vehicle entering the Luray Caverns has Canadian license plates is "A".
Let the event that a vehicle entering the Luray Caverns is a camper is denoted by "B".
Let the event that a vehicle entering the Luray Caverns is a camper with Canadian license plates is denoted by (AB).
So,
P(A)=0.19
P(B)=0.38
P(AB)=0.13
Step 2
(a) We find the probability that a camper entering the Luray Caverns has Canadian license plates as,
(AB)=P(AB)P(B)
=0.130.38
=0.3421
Hence, required probability is 0.3421.
(b) We find the probability that a vehicle with Canadian license plates entering the Luray Caverns is not a camper as,
P(BCA)=P(BCA)P(A)
=P(A)P(AB)P(A) [By formula, P(A)=P(AB)+P(BCA)]
=0.190.130.19
=0.3158
Hence, required probability is 0.3158.
(c) We find the probability that a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper is,
P(ACBC)=P(AB)C [By formula, P(ACBC)=P(AB)C]
=1P(AB)
=10.13
=0.87
Hence, required probability is 0.87.
Andre BalkonE

Andre BalkonE

Skilled2023-06-11Added 110 answers

(a) The probability that a camper entering the Luray Caverns has Canadian license plates can be calculated using the formula for conditional probability:
P(Canadian plates|camper)=P(Canadian platescamper)P(camper)
Given that P(Canadian plates)=0.19, P(camper)=0.38, and P(Canadian platescamper)=0.13, we can substitute these values into the formula:
P(Canadian plates|camper)=0.130.38=1338
(b) The probability that a vehicle with Canadian license plates entering the Luray Caverns is not a camper can be calculated using the complement rule. The complement of being a camper is being a non-camper. Therefore, the probability that a vehicle with Canadian license plates entering the Luray Caverns is not a camper is:
P(non-camper|Canadian plates)=1P(camper|Canadian plates)
Since we have already calculated P(camper|Canadian plates) in part (a), we can substitute its value into the formula:
P(non-camper|Canadian plates)=11338=2538
(c) The probability that a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper can be calculated by using the complement rule. The complement of having Canadian plates or being a camper is not having Canadian plates and being a camper. Therefore, the probability can be calculated as:
P(not Canadian plates or not camper)=1P(Canadian platescamper)
Since the probability that a vehicle is a camper with Canadian plates has already been given as 0.13, we can calculate the probability of not having Canadian plates and being a camper:
P(not Canadian plates and camper)=1P(Canadian platescamper)=10.13=0.87
Then, we can calculate the probability of not having Canadian plates or not being a camper:
P(not Canadian plates or not camper)=10.87=0.13

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