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Iridescent (talk | contribs) m Cleanup/typo fixing using AWB |
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Two different situations exemplify the interest in maximizing the probability to stop on a last specific event.
# Suppose a car is advertised for sale (best offer). n people respond and ask to see the car. They all insist that they would need the immediate decision whether their offer is accepted or not. Define an offer ''interesting'', coded ''1'' say, if it is better than all preceding offers, and coded ''0'' otherwise. The offers will form a random sequence of 0's and 1's. Only 1's are of interest to the seller, and with each 1 he/she may fear that there will be no further 1's. It follows from the definition that the very last 1 is the highest offer. Maximizing the probability of selling on the last 1 therefore means maximizing the probability of selling ''best''.▼
# A physician, using a special treatment, may use the code 1 for a successful treatment, 0 otherwise. Treating a sequence of n patients with the same treatment he/she wants to minimize unnecessary sufferings, and, at the same time, obtain ''all'' successes in the sequence of patients. Stopping on the last 1 in such a random sequence of 0's and 1's means to realize this objective. Since the physician has no prophetical power, his/her objective translates into the goal of finding a strategy maximizing the probability of stopping on the last 1.
▲that they would need the immediate decision whether their offer is accepted or not. Define an offer ''interesting'', coded ''1'' say, if it is better than all preceding offers, and coded ''0'' otherwise. The offers will form a random sequence of 0's and 1's. Only 1's are of interest to the seller, and with each 1 he/she may fear that there will be no further 1's. It follows from the definition that the very last 1 is the highest offer. Maximizing the probability of selling on the last 1 therefore means maximizing the probability of selling ''best''.
== Definitions ==
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