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A and B are highly truthful (they each tell the truth

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A and B are highly truthful (they each tell the truth [#permalink] New post 06 Dec 2003, 17:03
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27.A and B are highly truthful (they each tell the truth randomly 3/4 of
the time. Also, A's and B's truthfulness are independent. Suppose A and B both look out the window to see what the weather is like. A says, "It's raining." B says, "It's raining." What is the probability that it actually is raining.


my comment : do we need the probability of raining.
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 [#permalink] New post 06 Dec 2003, 20:32
stoolfi wrote:
15/16, if the chance of rain is 50/50.


could you explain please

whats happens with 50/50

and say.. with rain prob. = 25% and no rain prob. =75%

thanks
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 [#permalink] New post 06 Dec 2003, 21:15
Quote:
could you explain please?


chance of person A lying 1/4
chance of person B lying 1/4

Multiply to find chance of both lying:1/16
15/16, therefore, is the chance of both telling the truth.
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 [#permalink] New post 06 Dec 2003, 21:24
Quote:
whats happens with 50/50

and say.. with rain prob. = 25% and no rain prob. =75%


I don't know, exactly. But consider this:

Say it rains 1 day out of 160.
If you asked them, every day, whether it was raining, both of them would lie to you 10 times out of 160. So you've got a 1/160 chance of it raining, and an (approximate) 10/160 chance that they tell you it's raining. If they tell you it's raining, they're very probably lying.

I'm sure there's a way to figure this out in greater detail but that will probably not be on the GMAT.
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 [#permalink] New post 09 Dec 2003, 05:27
got 15/16
an event is telling the truth.
P=1-P(both lie)=1-1/16=15/16
  [#permalink] 09 Dec 2003, 05:27
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