Problem 12. Peter and Paula play a game of chance that consists of several rounds. Each...

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Problem 12. Peter and Paula play a game of chance that consistsof several rounds. Each individual round is won, with equalprobabilities, by either Peter or Paula; the winner then receivesone point. Successive rounds are independent. Each has staked 50for a total of 100, and they agree that the game ends as soon asone of them has won a total of 5 points; this player then receivesthe 100. After they have completed four rounds, of which Peter haswon three and Paula only one, a fire breaks out so that they cannotcontinue their game. How should the 100 be divided between Peterand Paula?

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answerPeter and Paula appear not to have conceded to how to continuewhen the amusement is hindered before one of them has won 5 pointsObviously at that point one alternative is that both basicallyhold their unique 50 in light of the fact that the diversion hasnot been finished by the principles initially conceded toThen again Peter may contend that he had officially gainedsignificant ground toward winning 5 and in this manner guaranteemore than his unique 50 A levelheaded premise of this case couldbe to consider in what number of comparable cases Peter wouldnally have prevailed upon Paula if the amusement hadproceeded All the more correctly Peter needs 2 more focusesthough Paula still needs twice the same number of to be specific4 In this way we may authentically ask what is the likelihoodthat Peter would have won the 2 required focuses before Paula hadwon 4The most difficult way possible to figure this likelihood is tocount every single conceivable succession that end positively forPeter and to aggregate their probabilities Note that Peterstriumph essentially closes with a point made by him and mightbegone before by 123 or at most 4 rounds of which Peter has wonprecisely one The entire rundown contains 10 conceivablearrangements of progressive champs A Peter wins a round B Paula wins a round AA ABA BAA ABBA BABA BBAA ABBBABABBA BBABA BBBAA and their probabilities are effectivelyfound to signify 2632 08125 This outcome proposes that Petermay guarantee 8125 in which case Paula gets 1875Unmistakably when the quantity of rounds that Peter and Paulawould in any case need to win gets biggerat that point this strategy of See Answer

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