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A jar contains 4 marbles: 2 red and 2 white. 2 marbles are

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SJ
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A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   Updated on: 07 Nov 2016, 01:29
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A jar contains 4 marbles: 2 red and 2 white. 2 marbles are chosen at random.

Quantity A
Quantity B
The probability that the marbles chosen are the same colour
The probability that the marbles chosen are different colours.



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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B

Originally posted by SJ on 06 Nov 2016, 13:06.
Last edited by Carcass on 07 Nov 2016, 01:29, edited 1 time in total.
Edited by Carcass
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sandy
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   06 Nov 2016, 13:36
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Here,

Quantity A:

P(The probability that the marbles chosen are the same color)= P(RED)*P(RED)+P(BLUE)*P(BLUE) = \(\frac{2}{4}*\frac{1}{3} + \frac{2}{4}*\frac{1}{3}\)

= \(\frac{1}{3}\)

Quantity B:

P(The probability that the marbles chosen are different colours) = P(RED)*P(BLUE)+P(BLUE)*P(RED)
=\(\frac{2}{4}*\frac{2}{3}+\frac{2}{4}*\frac{2}{3}\)
=\(\frac{2}{3}\)

Hence Quantity B is greater.
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   07 Nov 2016, 01:30
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Please follow the rules how to post a question

qq-how-to-post-a-gre-question-the-easy-way-2357.html

Thank you
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   13 Nov 2016, 07:30
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SJ wrote:
A jar contains 4 marbles: 2 red and 2 white. 2 marbles are chosen at random.

Quantity A
Quantity B
The probability that the marbles chosen are the same colour
The probability that the marbles chosen are different colours.




Here's a quick approach.

First pick 1 marble, ANY marble. For this first step, picking either color is equally likely.
At this point, there are 3 marbles remaining in the jar. 1 marble is the SAME color as the first marble you selected, and 2 marbles are a DIFFERENT color from the first marble you selected.
So, it's more likely that the two marbles will be DIFFERENT colors
Answer:
Show: ::
B


Mathematically, P(matching colors) = 1/3 and P(different colors) = 2/3
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   12 Oct 2021, 06:43
sandy wrote:
Here,

Quantity A:

P(The probability that the marbles chosen are the same color)= P(RED)*P(RED)+P(BLUE)*P(BLUE) = \(\frac{2}{4}*\frac{1}{3} + \frac{2}{4}*\frac{1}{3}\)

= \(\frac{1}{3}\)

Quantity B:

P(The probability that the marbles chosen are different colours) = P(RED)*P(BLUE)+P(BLUE)*P(RED)
=\(\frac{2}{4}*\frac{2}{3}+\frac{2}{4}*\frac{2}{3}\)
=\(\frac{2}{3}\)

Hence Quantity B is greater.


Why is 1W,1R not the same as 1R,1W?

If its random, why is it a permutation and not combination?
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GreenlightTestPrep
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   12 Oct 2021, 10:31
kairapotato wrote:
Why is 1W,1R not the same as 1R,1W?

If its random, why is it a permutation and not combination?


Here's a question that may help answer your question.

A bag contains 1 red marble and 1 white marble.
If you randomly select two marbles without replacement, what is the probability that the two marbles will be different colors?
Well, we know for certain that the probability is 1, since we can be guaranteed the two marbles will be different colors.

So when calculating the probability, we must treat WR and RW has different outcomes, otherwise are probability calculations
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   13 Oct 2021, 12:09
value of quant B = 4/4 * 3/4=3/4, right ?
because any marble is ok with us and next marble with same colour or not it doesn't matter, right ?
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   13 Oct 2021, 12:50
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void wrote:
value of quant B = 4/4 * 3/4=3/4, right ?
because any marble is ok with us and next marble with same colour or not it doesn't matter, right ?


See the explanation above by Brent. A bit of common sense will give you a fastest solution
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   24 Feb 2023, 02:01
Hi Bernt GreenlightTestPrep

2 marbles are a DIFFERENT color from the first marble you selected.
So, it's more likely that the two marbles will be DIFFERENT colors : 2/3

To clarify here have the question been 2R and 3W then the calculation will be as usual Probability calculation right?
Probability of different colour( 2/5 * 1/4)
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink] New post   24 Feb 2023, 04:39
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I think Brent explained how to handle the question in the following way very smart

Quote:
First pick 1 marble, ANY marble. For this first step, picking either color is equally likely.
At this point, there are 3 marbles remaining in the jar. 1 marble is the SAME color as the first marble you selected, and 2 marbles are a DIFFERENT color from the first marble you selected.
So, it's more likely that the two marbles will be DIFFERENT colors
Answer:
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Re: A jar contains 4 marbles: 2 red and 2 white. 2 marbles are [#permalink]
24 Feb 2023, 04:39
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