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# There are two kinds of books on the bookshelf: Spanish and

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Joined: 11 May 2008
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There are two kinds of books on the bookshelf: Spanish and [#permalink]

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05 Sep 2008, 18:55
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There are two kinds of books on the bookshelf: Spanish and English. If two books are randomly chosen from the bookshelf without replacement, what is the possibility that at least one of the books chosen is English book?
(1) The ratio of Spanish books to English book is 3:1
(2) There are less than 20 books on the shelf.
Director
Joined: 23 Sep 2007
Posts: 783

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05 Sep 2008, 20:33
arjtryarjtry wrote:
There are two kinds of books on the bookshelf: Spanish and English. If two books are randomly chosen from the bookshelf without replacement, what is the possibility that at least one of the books chosen is English book?
(1) The ratio of Spanish books to English book is 3:1
(2) There are less than 20 books on the shelf.

E

statement 1: insuff because it could be 3 spanish books to 1 english book, or 6 spanishs to 2 english, ....

statement 2: insuff

together: insuff because it could be --> 3 spanish books to 1 english book, OR 6 spanishs to 2 englishs, OR 9 to 3 OR 12 to 4.
VP
Joined: 17 Jun 2008
Posts: 1381

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05 Sep 2008, 20:33
arjtryarjtry wrote:
There are two kinds of books on the bookshelf: Spanish and English. If two books are randomly chosen from the bookshelf without replacement, what is the possibility that at least one of the books chosen is English book?
(1) The ratio of Spanish books to English book is 3:1
(2) There are less than 20 books on the shelf.

IMO E

(1) say ,3x spanish books,x english books => total=4x.
probability of getting atleast 1 english book = 1-probability of getting non english=1-(3x(3x-1)/4x(4x-1))as xvaries ,the prob varies.INSUFFI
(2)no clue about number of spanish and eng books INSUFFI

(1) and (2)now 4x<20 => x can be 4,3,2,1 we get different probabilties INSUFFI
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Joined: 03 Jun 2008
Posts: 137
Schools: ISB, Tuck, Michigan (Ross), Darden, MBS

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06 Sep 2008, 00:11
spriya wrote:
arjtryarjtry wrote:
There are two kinds of books on the bookshelf: Spanish and English. If two books are randomly chosen from the bookshelf without replacement, what is the possibility that at least one of the books chosen is English book?
(1) The ratio of Spanish books to English book is 3:1
(2) There are less than 20 books on the shelf.

IMO E

(1) say ,3x spanish books,x english books => total=4x.
probability of getting atleast 1 english book = 1-probability of getting non english=1-(3x(3x-1)/4x(4x-1))as xvaries ,the prob varies.INSUFFI
(2)no clue about number of spanish and eng books INSUFFI

(1) and (2)now 4x<20 => x can be 4,3,2,1 we get different probabilties INSUFFI

Nice explanation.
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Re: probability   [#permalink] 06 Sep 2008, 00:11
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# There are two kinds of books on the bookshelf: Spanish and

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