Difficult Math Problem #117 - Probability - The Beat The GMAT Forum

Difficult Math Problem #117 - Probability

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800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pmFollowed by: 5 members; Thanked: 11 times

by 800guy » Wed Apr 11, 2007 12:42 pm

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

A. 15/28

B. 1/4

C. 9/16

D. 1/32

E. 1/16

oa coming after some people respond, from diff math doc

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Source: Beat The GMAT — Problem Solving | Wed Apr 11, 2007 12:42 pm

guynoor: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Sat Feb 10, 2007 10:03 pm; Thanked: 1 times

Re: Difficult Math Problem #117 - Probability

by guynoor » Wed Apr 11, 2007 1:26 pm

800guy wrote:A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

A. 15/28

B. 1/4

C. 9/16

D. 1/32

E. 1/16

oa coming after some people respond, from diff math doc

I am a bit confused on this question too. I understand that the P of not selecting a Blue on the first draw is 3/4. But how is it that on the second draw the P of not selecting blue is 5/7 ???

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jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Wed Apr 11, 2007 9:21 pm

Probability of 1 Blue = 2/8 * 6/7 * 2 = 24 / 56
Probability of 2 Blue = 1 / 8C2 = 2/56

Hence probability of atleast 1 blue = Sum of above 2 prob = 26 / 56

Hence probability of no blue = 1 - 26/56 = 30/56 = 15/28

Is it A ?

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Neo2000: Legendary Member; Posts: 519; Joined: Sat Jan 27, 2007 7:56 am; Location: India; Thanked: 31 times

by Neo2000 » Wed Apr 11, 2007 9:47 pm

I like jayhawk's approach.

I actually worked it the other way around.

If NOT blue then you can get
1. Two Red
2. TWo Green
3. Two Yellow OR
4. 1R and 1G OR
5. 1G and 1Y OR
6. 1Y and 1R

Now picking 2 cards from 8 = 8C2 = 28

2R = 2C2 = 1
2G = 2C2 = 1
2Y = 2C2 = 1
1R and 1G = 2C1 x 2C1 = 4
1Y and 1G = 2C1 x 2C1 = 4
1R and 1Y = 2C1 x 2C1 = 4

So total = 15

Therefore probability = 15/28

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Thu Apr 12, 2007 3:23 am

First one is blue and second one is blue = 2/8 * 1/7 = 1/28
First one is blue and second one is other color = 2/8 * 6/7 = 6/28
First one is other color and second one is blue = 6/8 * 2/7 = 6/28

Thus neither is blue = 1 - (1/28 + 6/28 + 6/28)
= 1 - 13/28
= 15/28

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RAGS: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sun Mar 18, 2007 9:35 amFollowed by: 1 member; Location: mumbai

by RAGS » Thu Apr 12, 2007 5:14 am

the Q asks probability of both r not blue
I think the solutions provided here r for nither card drawn blue
Also the probability of both cards not blue is 27/28 which is not one of the options
Please reply if i am wrong

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800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pmFollowed by: 5 members; Thanked: 11 times

oa

by 800guy » Fri Apr 13, 2007 9:28 am

oa:

Chance of drawing a blue on the first draw = 2/8, so chance of not drawing a blue on the first draw is 6/8

similarly chance of not drawing blue on second draw = 5/7

Therefore probability of not drawing blue in 2 draws = 6/8*5/7 = 15/28

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alugoya: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 19, 2007 5:34 am

my approach

by alugoya » Fri Apr 13, 2007 12:57 pm

I would do it the following way

total out comes = 8c2 = 28

if none of the 2 cards drawn are blue(2 cards are drawn from the other 6 cards)...

so favourable events = 6c2 = 15

probability of not getting the blue card = 15/28

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon May 20, 2019 6:09 pm

800guy wrote:A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

A. 15/28

B. 1/4

C. 9/16

D. 1/32

E. 1/16

The probability that the first card will not be blue is 6/8 and that for the second is 5/7. Therefore, the probability that both cards will be non-blue is 6/8 x 5/7 = 30/56 = 15/28.

Answer: A

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