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A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another

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A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another  [#permalink]

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New post 27 Sep 2010, 15:25
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A
B
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D
E

Difficulty:

  65% (hard)

Question Stats:

48% (01:35) correct 53% (01:30) wrong based on 96 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
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Re: A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another  [#permalink]

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New post 27 Sep 2010, 15:44
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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Re: A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another  [#permalink]

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New post 27 Sep 2010, 15:47
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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Re: A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another  [#permalink]

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New post 27 Sep 2010, 20:50
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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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Re: A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another  [#permalink]

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New post 27 Sep 2010, 22:03
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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A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another  [#permalink]

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New post 24 Jan 2019, 15:52
Official answer:
Take the first bag of 100 marbles. 10 of the numbers overlap, so there is a 10/100 chance that there is a possibility of an overlap. (There’s a 90% chance already that the numbers will not be the same; for instance, that’s the case if the first marble drawn is numbered 72.) Once the first marble is drawn, the only way the two marbles will have the same number is if the second marble has exactly the same number. In other words, if we drew 96 from the first bag, we’re looking for the probability of drawing 96 from the second bag, as well. The probability of drawing a specific number from the second bag is 1/60. In order to draw the same marble from both bags, we need both of those events to happen, so we multiply the probabilities:
1/10 × 1/60 = 1/600, choice (D).
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A bag has 100 marbles numbered consecutively 0 - 99 inclusive. Another   [#permalink] 24 Jan 2019, 15:52
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