SOLUTION: the odds in favor of Trudy beating her friend in a round of golf are 1:9. Find the probability that Trudy will lose.

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Question 166315: the odds in favor of Trudy beating her friend in a round of golf are 1:9. Find the probability that Trudy will lose.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the odds in favor of Trudy beating her friend in a round of golf are 1:9. Find the probability that Trudy will lose.
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Formula: "odds FOR event A" = P(A)/P(not A)
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Your Problem:
1:9 = P(A)/P(not A)
P(A) = (1/9)*P(not A)
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But P(A) + P(not A) = 1
So, P(not A) = 1 - P(A)
And P(not A) = 1 - [(1/9)P(not A)]
(10/9)P(not A) = 1
P(not A) = 9/10
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That was a bit long-winded. Here's a shorter version.
Since odds FOR = 1:9
P(A) = 1/(1+9) = 1/10
So P(A') = 9/10
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Cheers,
Stan H.