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Onell
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A license plate in the country Kerrania consists of four digits follow Updated on: 24 Jul 2016, 08:13
Originally posted by Onell on 15 Mar 2011, 22:50.
Last edited by Bunuel on 24 Jul 2016, 08:13, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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D
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45% (medium)

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70% (02:41) correct 30% (02:57) wrong based on 231 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-license-plate-in-the-country-kerrania-consists-of-four-digits-follow-187749.html
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D
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bagrettin
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A license plate in the country Kerrania consists of four digits follow 16 Mar 2011, 01:14
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Since it is a government vehicle, then only 3 letters could be used: A, B, C. Therefore the possible options for letter part of a license plate are: AB, AC, BC, BA, CA, CB - 6 options. The plate has 79 at the beginning, and 2 other digits from 0 to 9, so all possibilities are 00..99 - 100 overall. Fnally, there are 600 possible vehicles (6 letter options and 100 digit options for each combination). Within 3 hours the policy will inspect 18 vehicles, so the final probability is 18/600=3/100
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A license plate in the country Kerrania consists of four digits follow 16 Mar 2011, 01:21
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bagrettin
Since it is a government vehicle, then only 3 letters could be used: A, B, C. Therefore the possible options for letter part of a license plate are: AB, AC, BC, BA, CA, CB - 6 options. The plate has 79 at the beginning, and 2 other digits from 0 to 9, so all possibilities are 00..99 - 100 overall. Fnally, there are 600 possible vehicles (6 letter options and 100 digit options for each combination). Within 3 hours the policy will inspect 18 vehicles, so the final probability is 18/600=3/100
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bagrettin - I also thought the same initially, but I think what is missing is that the two alphabets can also be same, so three more cases of AA, BB and CC also need to be included. In that case, the probability becomes 18/900 or 1/50
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bagrettin
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A license plate in the country Kerrania consists of four digits follow 16 Mar 2011, 01:24
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Oh, yes! You are ABSOLUTELY RIGHT!
Here we could have repeated letters.
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A license plate in the country Kerrania consists of four digits follow 16 Mar 2011, 01:40
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bagrettin
Since it is a government vehicle, then only 3 letters could be used: A, B, C. Therefore the possible options for letter part of a license plate are: AB, AC, BC, BA, CA, CB - 6 options. The plate has 79 at the beginning, and 2 other digits from 0 to 9, so all possibilities are 00..99 - 100 overall. Fnally, there are 600 possible vehicles (6 letter options and 100 digit options for each combination). Within 3 hours the policy will inspect 18 vehicles, so the final probability is 18/600=3/100
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Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.

Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/10 = 18

P = 18/900 = 1/50

Ans: "D"
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A license plate in the country Kerrania consists of four digits follow 17 Mar 2011, 01:15
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1 * 1 * 10 * 10 * 3 * 3 = 900 numbers

=> 900 * 10 minutes = 9000

So Prob = 3 * 60/9000 = 18/900 = 1/50

Answer is D.
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A license plate in the country Kerrania consists of four digits follow 18 Mar 2011, 11:36
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bagrettin
Since it is a government vehicle, then only 3 letters could be used: A, B, C. Therefore the possible options for letter part of a license plate are: AB, AC, BC, BA, CA, CB - 6 options. The plate has 79 at the beginning, and 2 other digits from 0 to 9, so all possibilities are 00..99 - 100 overall. Fnally, there are 600 possible vehicles (6 letter options and 100 digit options for each combination). Within 3 hours the policy will inspect 18 vehicles, so the final probability is 18/600=3/100

bagrettin - I also thought the same initially, but I think what is missing is that the two alphabets can also be same, so three more cases of AA, BB and CC also need to be included. In that case, the probability becomes 18/900 or 1/50
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hehehe INTERLLOGENT you ARE! hehehe... yes, thanks, forgot AA BB and CC could be included
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A license plate in the country Kerrania consists of four digits follow 22 Mar 2011, 09:15
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Thanks guys for your help ... OA is D
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A license plate in the country Kerrania consists of four digits follow 01 May 2011, 23:41
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10*10*3*3= total combinations = 900 vehicles.
in 180 minutes,if it takes 10 mints for each vehicle then total vehicles inspected = 18.

Thus 18/900 = 1/50
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A license plate in the country Kerrania consists of four digits follow 24 Jul 2016, 08:14
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Onell
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
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OPEN DISCUSSION OF THIS QUESTION IS HERE: a-license-plate-in-the-country-kerrania-consists-of-four-digits-follow-187749.html
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