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# Chances of A saying the truth is 70% and B saying the truth

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GMAT Club Legend
Joined: 15 Dec 2003
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Chances of A saying the truth is 70% and B saying the truth [#permalink]  08 Nov 2004, 18:57
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Chances of A saying the truth is 70% and B saying the truth is 40%. Replying to a question what are the chances that they will contradict each other?

(1) 45% (2) 60% (3) 28% (4) None
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Joined: 16 Jun 2004
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Kudos [?]: 19 [0], given: 0

7/10*6/10 + 3/10*4/10 = 54/100 = 54%.

I only see a 45%. Is that a typo or is it E. I will go with E...since I dont see a 54%.
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Joined: 21 Jun 2004
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Kudos [?]: 2 [0], given: 0

Probability of A saying the truth : P(A)=7/10
Probability of A not saying the truth : P(A')=3/10

Probability of B saying the truth : P(B)=4/10
Probability of B not saying the truth : P(B')=6/10

Proobability that they will contradict each other:

P(A).P(B') + P(B).P(A')=7/10*6/10 +4/10*3/10
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Joined: 08 Nov 2004
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Kudos [?]: 0 [0], given: 0

Re: PS Truth or Lie? [#permalink]  08 Nov 2004, 22:55
They will contradict each other means A tells the truth, and B lies OR A lies and B tells the truth

(0.7 * 0.6) + (0.3 * 0.4) = 0.42 + 0.12 = 0.54 or answer choice (4)
Re: PS Truth or Lie?   [#permalink] 08 Nov 2004, 22:55
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