Question 190261: can someone please help..thanks
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 ? .1574
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
What is the probability that the wildcats win the series in 4 games? .156
what is the probability that the bears win the series in 5 games?
what is the probability that the wildcats win the series in 5 games?
What is the probability that the bears win the series?
what is the probability that the wildcats win the series ?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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