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# A box contains 4 red chips and 2 blue chips. If two chips ar

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Director
Joined: 25 Oct 2008
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Location: Kolkata,India
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A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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29 Oct 2009, 02:15
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Difficulty:

5% (low)

Question Stats:

92% (02:03) correct 8% (01:08) wrong based on 193 sessions

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A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10

............................................................
My solution:
Got the correct answer by the following method.
(4/6)(2/5)+(2/6)(4/5)= 8/15>>OA

My querie:
Why are we not getting the answer when we do 1-same color??
1-Both red + 1-both blue
(4/6)(3/6)+(2/6)(1/6)
[Reveal] Spoiler: OA

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http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 85571 [2] , given: 10237

Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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29 Oct 2009, 02:40
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tejal777 wrote:
Guys please tell me where am i going wrong:

A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

............................................................
My solution:
Got the correct answer by the following method.
(4/6)(2/5)+(2/6)(4/5)= 8/15>>OA

My querie:
Why are we not getting the answer when we do 1-same color??
1-Both red + 1-both blue
(4/6)(3/6)+(2/6)(1/6)

First solution is right.

As for the second one: you've made a little mistake you've avoided when solving for the different colors.

We surely can get the answer for same color by exactly the same method:

P(both same color)=4/6*3/5+2/6*1/5

You just forgot that when taking the first chip there are 5 left, so the chances of getting is out of 5, not out of 6.

Hope it's clear.
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Director
Joined: 25 Oct 2008
Posts: 608
Location: Kolkata,India
Followers: 11

Kudos [?]: 722 [0], given: 100

Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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29 Oct 2009, 03:25
thank you..I'll go jump off the balcony now..!!grumble grumble..Silly silly!!
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http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

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Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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18 Jan 2011, 10:55
1
KUDOS
Total selection ways: 6C2=6!/2!4!=15
Selecting one blue chip out of two: 2C1=2!/1!1!=2
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (2C1*4C1)/6C2=(2*4)/15=8/15
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Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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25 Oct 2013, 07:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Joined: 17 Jul 2014
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Location: United States
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A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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14 Oct 2014, 13:23
1
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can someone explain if the method used by me is correct?

we have 6 chips, and out of which we have to select 2, hence 6C2=15
we have 4 red chips - 4C1=4
2 blue chips - 2C1=2
then we multiply the combinations 4x2 and get 8
putting all together, we have the probability of selecting one red and one blue - 8/15

Last edited by mvictor on 14 Oct 2014, 13:29, edited 3 times in total.
SVP
Joined: 17 Jul 2014
Posts: 1847
Location: United States
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 15

Kudos [?]: 217 [0], given: 114

Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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14 Oct 2014, 13:39
Bunuel, can u pls specify if my method is good to use for solving this problem
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Kudos [?]: 85571 [0], given: 10237

Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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14 Oct 2014, 13:56
mvictor wrote:
can someone explain if the method used by me is correct?

we have 6 chips, and out of which we have to select 2, hence 6C2=15
we have 4 red chips - 4C1=4
2 blue chips - 2C1=2
then we multiply the combinations 4x2 and get 8
putting all together, we have the probability of selecting one red and one blue - 8/15

Yes, that's correct.
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Joined: 09 Sep 2013
Posts: 12213
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Re: A box contains 4 red chips and 2 blue chips. If two chips ar [#permalink]

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09 Dec 2015, 14:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: A box contains 4 red chips and 2 blue chips. If two chips ar   [#permalink] 09 Dec 2015, 14:55
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# A box contains 4 red chips and 2 blue chips. If two chips ar

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