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24 Aug 2010, 09:30
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D
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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
OA is D which I got it the first time but the it seemed too "simplistic" and then I got confused. S as per my understanding shouldnt the denominator be 171 rather than 8?
171 is derived by assuming that car is found within the first 10 minutes - 1 attempt
Car is found during second attempt : 2 attempts
Car is found during thrid attempt : 3 attempts
.............
............
Car is found in 18th attempt ; 18 attempts
We sum them all up to get 171 and divide it by 900 to get the probability? It is sort of like having first success in nth attempt kind of question so all paths to reach there should be accounted for ?
Help will be appreciated
A) 18/79
B) 1/6
C) 1/25
D) 1/50
E) 1/900
OA is D which I got it the first time but the it seemed too "simplistic" and then I got confused. S as per my understanding shouldnt the denominator be 171 rather than 8?
171 is derived by assuming that car is found within the first 10 minutes - 1 attempt
Car is found during second attempt : 2 attempts
Car is found during thrid attempt : 3 attempts
.............
............
Car is found in 18th attempt ; 18 attempts
We sum them all up to get 171 and divide it by 900 to get the probability? It is sort of like having first success in nth attempt kind of question so all paths to reach there should be accounted for ?
Help will be appreciated
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24 Aug 2010, 09:48
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So there are 900 cars that they have to search.. Each takes 10mins, total of 9000 mins.. Have to find in 180 mins.. Prob180/9000 = 1/50
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24 Aug 2010, 09:59
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#of cars to search: 900 (we know the first two numbers and the fact that it's a gov't. vehicle, so the number of possibilities is 10 x 10 x 3 x 3).
10 minutes per inspection = 6 inspections/min
3 hours @ 6 inspections/min = 18 inspections.
18 inspections out of 900 possible vehicles = 18/900 = 1/50
10 minutes per inspection = 6 inspections/min
3 hours @ 6 inspections/min = 18 inspections.
18 inspections out of 900 possible vehicles = 18/900 = 1/50
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
