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# GRE Math Challenge #83-The odds in favor of winning a game

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GRE Math Challenge #83-The odds in favor of winning a game [#permalink]  09 May 2015, 10:24
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Question Stats:

100% (00:29) correct 0% (00:00) wrong based on 4 sessions
The odds in favor of winning a game can be found by computing the ratio of the probability of wining to the probability of not winning. if the probability that Pat will win a game is 4/9 , what are the odds that Pat will win the game?

(A) 4 to 5
(B) 4 to 9
(C) 5 to 4
(D) 5 to 9
(E) 9 to 5
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #83-The odds in favor of winning a game [#permalink]  14 Dec 2017, 08:49
sandy wrote:
The odds in favor of winning a game can be found by computing the ratio of the probability of wining to the probability of not winning. if the probability that Pat will win a game is 4/9 , what are the odds that Pat will win the game?

(A) 4 to 5
(B) 4 to 9
(C) 5 to 4
(D) 5 to 9
(E) 9 to 5

Here odds in favor of winning a game = $$\frac{probability of wining}{probability of not winning}$$.

Now,
Let W =probability of wining

and N=probability of not winning

Since probability of winning the game W = $$\frac{4}{9}$$,

Therefore the probability of not winning a game N = $$\frac{5}{9}$$ $$(1-\frac{4}{9})$$

Hence the odds in favor of winning a game = $$\frac{W}{N}$$ = $$\frac{4}{9} * \frac{9}{5}$$ = $$\frac{4}{5}$$
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Re: GRE Math Challenge #83-The odds in favor of winning a game   [#permalink] 14 Dec 2017, 08:49
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