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A license plate in the country Kerrania consists of four digits follow
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04 Jun 2021, 23:03
04 Jun 2021, 23:03
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A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 10 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900
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Re: A license plate in the country Kerrania consists of four digits follow
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06 Jun 2021, 23:49
06 Jun 2021, 23:49
1
GeminiHeat wrote:
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 10 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900
(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900
License Plate pattern: DDDDAA
Where,
D can be from 0-9
A (for govt.) = 3
A (for non govt.) = 23
Now, an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79
i.e. the license plate will be something like - 79DD(3)(3)
we can pick 10 numbers for D
Therefore, 79(10)(10)(3)(3) = 900 plates need to be inspected
Total time required for inspection = (900)10 = 9000 minutes
The required Probability = \(\frac{3hours}{9000minutes} = \frac{180}{9000} = \frac{1}{50}\)minutes
Hence, option D
gmatclubot
Re: A license plate in the country Kerrania consists of four digits follow [#permalink]
06 Jun 2021, 23:49
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