SOLUTION: Four women’s college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of "1.70 to 1
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Question 1195030: Four women’s college basketball teams are participating in a single-elimination holiday basketball tournament. If one team is favored in its semifinal match by odds of "1.70 to 1.30" and another squad is favored in its contest by odds of "2.60 to 1.40", what is the probability that:
a. Both favored teams win their games? (Round your answer to 2 decimal places.)
b. Neither favored team wins its game? (Round your answer to 4 decimal places.)
c. At least one of the favored teams wins its game? (Round your answer to 4 decimal places.)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The odds in favor of the first team's winning being 1.70:1.30 means the probability of its winning is 1.70/(1.70+1.30)=1.70/3.00 = 17/30. Then the probability that that team loses is 13/30.
Similarly, for the second team, the odds in favor of winning of 2.60:1.40 means its probability of winning is 26/40=13/20 and its probability of losing is 7/20.
Then....
a. Both win:
(17/30)(13/20)=221/600
b. Neither wins:
(13/30)(7/20) = 91/600
c. At least one wins:
1 minus the probability that neither wins: 1 - 91/600 = 509/600
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