me probability that the heaviest truck in a su

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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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