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me probability that the heaviest truck in a su

me probability that the heaviest truck in a su

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 84CR
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any help would be much appreciated thanks

9. There is a queue of a total of N trucks waiting to pass through a check point. Each truck has a weight which will be checked at the moment of passing through the check point. (a) Derive an expression for the probability that the heaviest truck in a sub-set of n trucks (i.e. where n < N) is also the heaviest truck in the entire set of N trucks. (For visualization purposes, one can imagine a queue of N = 100 trucks, and a driver of one truck who can see just n = 10 trucks in the queue, including their own truck. However, the answers being sought are for any values of N and n.) (b) Determine the probability that the heaviest truck in a sub-set of n trucks is either the heaviest or second heaviest truck in the entire set of N trucks. (c) Check your result from (b) for the case of N = 4 and n = 2 by writing out the possible queues and marking the ones which satisfy (b).
Transcribed Image Text:9. There is a queue of a total of N trucks waiting to pass through a check point. Each truck has a weight which will be checked at the moment of passing through the check point. (a) Derive an expression for the probability that the heaviest truck in a sub-set of n trucks (i.e. where n < N) is also the heaviest truck in the entire set of N trucks. (For visualization purposes, one can imagine a queue of N = 100 trucks, and a driver of one truck who can see just n = 10 trucks in the queue, including their own truck. However, the answers being sought are for any values of N and n.) (b) Determine the probability that the heaviest truck in a sub-set of n trucks is either the heaviest or second heaviest truck in the entire set of N trucks. (c) Check your result from (b) for the case of N = 4 and n = 2 by writing out the possible queues and marking the ones which satisfy (b).
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