Using the algorithm series of Section 8.1.2, calculate the probability that team A will win the series if p=0.45 and if

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Using the algorithm series of Section 8.1.2, calculate the
probability that team A will win the series if p=0.45 and if four
victories are needed to win.

Using The Algorithm Series Of Section 8 1 2 Calculate The Probability That Team A Will Win The Series If P 0 45 And If 1 (207.73 KiB) Viewed 16 times

8.1.2 The World Series Imagine a competition in which two teams A and B play not more than 2n - 1 a games, the winner being the first team to achieve n victories. We assume that there are no tied games, that the results of each match are independent, and that for any given match there is a constant probability p that team A will be the winner, and hence a constant probability 4 = 1-p that team B will win. Let Pli,j) be the probability that team A will win the series given that they still need i more victories to achieve this, whereas team B still need j more victories if they are to win. For example, before the first game of the series the probability that team A will be the overall winner is Pin, n): both teams still need n victories to win the series. If team A require 0 more victories, then in fact they have already won the series, and so P(0,1)= 1, 1 sis n. Similarly if team B require 0 more victories, then they have already won the series, and the probability that team A will be the overall winners is zero: so P(1,0)= 0, 1 sisn. Since there cannot be a situation where both teams have won all the matches they need, P(0,0) is meaningless. Finally, since team A win any given match with probability p and lose it with probability 9, Pli, j)= pPli-1.j)+ P(i, j - 1), i21, 121. Thus we can compute Pli, j) as follows. function Pli, j) if i = 0 then return 1 else if j = 0 then return 0 else return pP(i-1,1)+qP(i, j - 1)