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# A reader searches a sertain book in three libraries

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Joined: 03 Feb 2003
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A reader searches a sertain book in three libraries [#permalink]  03 Aug 2003, 02:16
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A reader searches a sertain book in three libraries. The probability that any library has the book equals to the probability that the library does not. The probability that the book is available in any library equals to the probability that the book is not. What is the probability that the reader will find the book?
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Joined: 07 Jul 2003
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Take a look at one library
P the library has the book 1/2
P the book is available there is 1/2
So the chances of finding the book 1/2*1/2=1/4
If he does not find it there he goes to second
P of finding in the second library including P not finding in the first
1/4*3/4=3/16
and so on...
P=1/4+(1/4*3/4)+(3/4*3/4*1/4)=37/64
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