Question 190261
Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. Let's suppose that for each game they play, the probability that the Bears win is 0.54 and the probability the Wildcats win is 0.46.
What is the probability that the bears win the series in 3 games ? .1575
What is the probability that the wildcats win the series in 3 games? .0973
What is the probability that the bears win the series in 4 games? .216
Patterns are LWWW, WLWW, WWLW 
Each has probability (0.54^3)(0.46)= 0.07243
But all three are mutually exclusive so the probability = 3(0.07243) 
= 0.2173
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What is the probability that the wildcats win the series in 4 games? .156
Prob = 3*0.46^3*0.54 = 0.1577
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what is the probability that the bears win the series in 5 games?
# of patterns: 5C2 - 1= 10-1 = 9
Probability of each pattern = (0.54)^3(0.46)^2 = 0.03332
Ans: 9*0.3332 = 0.2999
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what is the probability that the wildcats win the series in 5 games?
Ans: 9*(0.46)^3(0.54)^2 = 0.2747
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What is the probability that the bears win the series?
They could win it in 4, or 5, or 6, or 7 games.
Figure each probability and add them.
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what is the probability that the wildcats win the series ?
Same process as with the bears winning.
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Cheers,
Stan H.