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

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CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 703 [0], given: 781

A and B are highly truthful (they each tell the truth [#permalink]  06 Dec 2003, 16:03
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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.
CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 703 [0], given: 781

stoolfi wrote:
15/16, if the chance of rain is 50/50.

whats happens with 50/50

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

thanks
praetorian
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

Quote:

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.
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

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.
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

got 15/16
an event is telling the truth.
P=1-P(both lie)=1-1/16=15/16
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