Tricky Probability : GMAT Problem Solving (PS)
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# Tricky Probability

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Director
Joined: 07 Jun 2004
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27 Sep 2010, 14:25
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Difficulty:

35% (medium)

Question Stats:

73% (01:40) correct 27% (00:49) wrong based on 11 sessions

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A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another bag has 60 marbles numbered consecutively 90 - 149 inclusive. If a marble is randomly chosen from each bag, what is the probability that two marbles have the same number

1/10

1/60

1/100

1/600

1/6000
[Reveal] Spoiler: OA

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27 Sep 2010, 14:44
rxs0005 wrote:
A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another bag has 60 marbles numbered consecutively 90 - 149 inclusive. If a marble is randomly chosen from each bag, what is the probability that two marbles have the same number

1/10

1/60

1/100

1/600

1/6000

Common numbers : 90,91...99 total 10 numbers

probability = $$\frac{10}{{100*60}}$$ = $$\frac{1}{{600}}$$ = D
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27 Sep 2010, 14:47
No of ways to pick two marbles = 100*60 = 6000

No of ways to pick same number = (90,90) , ... , (99,99) = 10

So probability = 1/600
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27 Sep 2010, 19:50
rxs0005 wrote:
A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another bag has 60 marbles numbered consecutively 90 - 149 inclusive. If a marble is randomly chosen from each bag, what is the probability that two marbles have the same number

1/10

1/60

1/100

1/600

1/6000

My approach:

Pickup the matching 10 numbered marbles from the first bag -- Probability - 10/100 -- 1/10

Now we have one of the marble numbered from 90 - 99. From the other bag we need to pick just the one marble which will have a number from 90 - 99 to ensure we have a matching marble set. Its probability is 1/60.

Hence combined probability is (1/10) * (1/60) -- 1/600. Answer D.

There is a similar question in this forum , check this out -- http://gmatclub.com/forum/junior-58914.html
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27 Sep 2010, 21:03
ezhilkumarank wrote:
rxs0005 wrote:
A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another bag has 60 marbles numbered consecutively 90 - 149 inclusive. If a marble is randomly chosen from each bag, what is the probability that two marbles have the same number

1/10

1/60

1/100

1/600

1/6000

My approach:

Pickup the matching 10 numbered marbles from the first bag -- Probability - 10/100 -- 1/10

Now we have one of the marble numbered from 90 - 99. From the other bag we need to pick just the one marble which will have a number from 90 - 99 to ensure we have a matching marble set. Its probability is 1/60.

Hence combined probability is (1/10) * (1/60) -- 1/600. Answer D.

There is a similar question in this forum , check this out -- http://gmatclub.com/forum/junior-58914.html

my approach.....

probability of picking a marble from 0 -99 in the first set = 1/100 { since 0-99 is hundred marbles}

similarly, probability of picking a marble from 90-149 in the second set = 1/60

therefore, probability that they are same = (1/100) * (1/60) = 1/6000

it can happen for 10 marbles ( 90 to 99 inclusive ) .

Thus, total probability = 10 *1/6000 = 1/600 ANS
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Re: Tricky Probability   [#permalink] 27 Sep 2010, 21:03
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