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The probability of winning game A is X and the probability of winning

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The probability of winning game A is X and the probability of winning [#permalink]

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New post 29 Sep 2016, 04:38
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The probability of winning game A is X and the probability of winning game B is Y. When playing a single round of each of the two games, what is the probability of winning exactly once?

A. X-YX
B. XY
C. X+Y
D. X+Y-2XY
E. X^2Y^2-XY^2-X^2Y

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Re: The probability of winning game A is X and the probability of winning [#permalink]

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New post 29 Sep 2016, 07:21
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Probability of winning exactly once --> A wins and B loses or A loses and B wins
= X(1 - Y) + (1 - X)Y
= X - XY + Y - XY
= X + Y - 2XY

Answer: D
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Re: The probability of winning game A is X and the probability of winning [#permalink]

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New post 29 Sep 2016, 12:54
I picked numbers

X=1/3
Y=1/4

Probability of winning A and losing B (1/3)*(3/4)=1/4
Probability of losing A and winning B (2/3)*(1/4)=1/6

Because it is either option A OR option B we add the two probabilities together

1/4+1/6=5/12. If you plug the numbers back into the answer choices you will get D.
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Re: The probability of winning game A is X and the probability of winning [#permalink]

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New post 27 Feb 2017, 04:24
P(game A win) = X, P(game A lose) = 1-X
P(game B win) = Y, P(game B lose) = 1-Y
P(exactly one game win = P(game A win) P(game B lose) + P(game B win) P(game A lose) = X(1-Y) + Y(1-X) = X +Y -2XY. Option D
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Re: The probability of winning game A is X and the probability of winning [#permalink]

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New post 13 Mar 2017, 21:16
Bunuel wrote:
The probability of winning game A is X and the probability of winning game B is Y. When playing a single round of each of the two games, what is the probability of winning exactly once?

A. X-YX
B. XY
C. X+Y
D. X+Y-2XY
E. X^2Y^2-XY^2-X^2Y


Hi,

I used the following approach :
P(Winning A) = X
P(Winning B) = Y
p(Winning Both) = X.Y

Total = X+Y-XY

Kindly suggest where I'm going wrong.
Re: The probability of winning game A is X and the probability of winning   [#permalink] 13 Mar 2017, 21:16
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