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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
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A license plate in the country Kerrania consists of four digits follow...
Since the first two digits of the license plate are known and there are 10 possibilities for each of the remaining two digits (each can be any digit from 0 to 9), the total number of combinations for digits on the license plate will equal 10 ×10 = 100.
Because there are only 3 letters that can be used for government license plates (A, B, or C), there are a total of nine two-letter combinations that could be on the license plate (3 possibilities for first letter × 3 possibilities for the second letter).
Given that we have 100 possible digit combinations and 9 possible letter combinations, the total number of vehicles to be inspected will equal 100 × 9 = 900. Since it takes 10 minutes to inspect one vehicle, the police will have time to inspect 18 vehicles in three hours (3 hours = 180 minutes). Thus, the probability of locating the transmitter within the allotted time is 18/900 = 1/50.
Because there are only 3 letters that can be used for government license plates (A, B, or C), there are a total of nine two-letter combinations that could be on the license plate (3 possibilities for first letter × 3 possibilities for the second letter).
Given that we have 100 possible digit combinations and 9 possible letter combinations, the total number of vehicles to be inspected will equal 100 × 9 = 900. Since it takes 10 minutes to inspect one vehicle, the police will have time to inspect 18 vehicles in three hours (3 hours = 180 minutes). Thus, the probability of locating the transmitter within the allotted time is 18/900 = 1/50.
Most Upvoted Answer
A license plate in the country Kerrania consists of four digits follow...
To find the probability that the police will find the transmitter within three hours, we need to determine the total number of government vehicles that can be inspected within that time frame.
1. Total number of government vehicles:
Since the license plate starts with 79, the first two digits are fixed. The remaining two digits can be any number from 0 to 9, giving us a total of 10 possibilities. The two letters can be any from A, B, and C, giving us a total of 3 possibilities.
Therefore, the total number of government vehicles is 10 * 10 * 3 = 300.
2. Total time to inspect a vehicle:
Given that it takes 10 minutes to inspect each vehicle, the total time required to inspect 300 vehicles is 300 * 10 = 3000 minutes.
3. Probability of finding the transmitter within three hours:
Three hours is equal to 180 minutes.
The probability of finding the transmitter within three hours is equal to the ratio of the time required to inspect the vehicles within three hours to the total time required to inspect all vehicles.
Therefore, the probability is 180 / 3000 = 1/16.
However, none of the provided answer options match the calculated probability. Let's recheck our calculations.
4. Rechecking the calculations:
The total time required to inspect 300 vehicles is 300 * 10 = 3000 minutes, which is correct.
The probability of finding the transmitter within three hours is equal to the ratio of the time required to inspect the vehicles within three hours to the total time required to inspect all vehicles.
Therefore, the probability is 180 / 3000 = 3/50.
Now, we can see that the correct answer is not among the provided options. None of the options match the calculated probability of 3/50. Therefore, the given answer options are incorrect or there might be an error in the question itself.
1. Total number of government vehicles:
Since the license plate starts with 79, the first two digits are fixed. The remaining two digits can be any number from 0 to 9, giving us a total of 10 possibilities. The two letters can be any from A, B, and C, giving us a total of 3 possibilities.
Therefore, the total number of government vehicles is 10 * 10 * 3 = 300.
2. Total time to inspect a vehicle:
Given that it takes 10 minutes to inspect each vehicle, the total time required to inspect 300 vehicles is 300 * 10 = 3000 minutes.
3. Probability of finding the transmitter within three hours:
Three hours is equal to 180 minutes.
The probability of finding the transmitter within three hours is equal to the ratio of the time required to inspect the vehicles within three hours to the total time required to inspect all vehicles.
Therefore, the probability is 180 / 3000 = 1/16.
However, none of the provided answer options match the calculated probability. Let's recheck our calculations.
4. Rechecking the calculations:
The total time required to inspect 300 vehicles is 300 * 10 = 3000 minutes, which is correct.
The probability of finding the transmitter within three hours is equal to the ratio of the time required to inspect the vehicles within three hours to the total time required to inspect all vehicles.
Therefore, the probability is 180 / 3000 = 3/50.
Now, we can see that the correct answer is not among the provided options. None of the options match the calculated probability of 3/50. Therefore, the given answer options are incorrect or there might be an error in the question itself.
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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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer?
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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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer?.
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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)18/79b)1/6c)1/25d)1/50e)1/900Correct answer is option 'D'. Can you explain this answer?.
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