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# A box contains three pairs of blue gloves and two pairs of

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Senior Manager
Joined: 03 Apr 2013
Posts: 289
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
GMAT 1: 740 Q50 V41
GPA: 3
Re: A box contains three pairs of blue gloves and two pairs of [#permalink]

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11 Jul 2017, 01:23
Bunuel wrote:
arps wrote:
A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

(A) 3/10
(B) 23/60
(C) 7/12
(D) 41/60
(E) 5/6

Let's calculate the opposite probability of NOT getting a matched set and subtract this value from 1.

This could happen only if we pick all three same hand BLUE gloves; two same hand BLUE gloves and any green glove; or two same hand GREEN gloves and any BLUE glove

BBB: $$\frac{6}{10}*\frac{2}{9}*\frac{1}{8}=\frac{1}{60}$$ (after we pick a blue glove, 6/10, then there is 2 same hand gloves left out of total 9 gloves - 2/9, and so on);

BBG: $$(\frac{6}{10}*\frac{2}{9}*\frac{4}{8})*3=\frac{12}{60}$$, multiplying by 3 as this scenario can occur in 3 different ways: BBG, BGB, GBB;

GGB: $$(\frac{4}{10}*\frac{1}{9}*\frac{6}{8})*3=\frac{6}{60}$$;

$$P=1-(\frac{1}{60}+\frac{12}{60}+\frac{6}{60})=\frac{41}{60}$$.

hope it's clear.

Dear Bunuel, questions of this type actually give me hell.

I face problems in identifying what is unique or identical and what's not!

Here I at first thought that the socks of the same color and foot were identical, but I don't know if that's true. Then I thought that every pair is unique, which I also don't know. Please help me on how to comprehend questions of this type. How to actually translate and understand what's unique and what's not? VeritasPrepKarishma your inputs are also most welcome.
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8058
Location: Pune, India
Re: A box contains three pairs of blue gloves and two pairs of [#permalink]

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12 Jul 2017, 01:43
ShashankDave wrote:
Bunuel wrote:
arps wrote:
A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

(A) 3/10
(B) 23/60
(C) 7/12
(D) 41/60
(E) 5/6

Let's calculate the opposite probability of NOT getting a matched set and subtract this value from 1.

This could happen only if we pick all three same hand BLUE gloves; two same hand BLUE gloves and any green glove; or two same hand GREEN gloves and any BLUE glove

BBB: $$\frac{6}{10}*\frac{2}{9}*\frac{1}{8}=\frac{1}{60}$$ (after we pick a blue glove, 6/10, then there is 2 same hand gloves left out of total 9 gloves - 2/9, and so on);

BBG: $$(\frac{6}{10}*\frac{2}{9}*\frac{4}{8})*3=\frac{12}{60}$$, multiplying by 3 as this scenario can occur in 3 different ways: BBG, BGB, GBB;

GGB: $$(\frac{4}{10}*\frac{1}{9}*\frac{6}{8})*3=\frac{6}{60}$$;

$$P=1-(\frac{1}{60}+\frac{12}{60}+\frac{6}{60})=\frac{41}{60}$$.

hope it's clear.

Dear Bunuel, questions of this type actually give me hell.

I face problems in identifying what is unique or identical and what's not!

Here I at first thought that the socks of the same color and foot were identical, but I don't know if that's true. Then I thought that every pair is unique, which I also don't know. Please help me on how to comprehend questions of this type. How to actually translate and understand what's unique and what's not? VeritasPrepKarishma your inputs are also most welcome.

The question gives you clues:

"Each pair consists of a left-hand glove and a right-hand glove."

Shows that the gloves in a pair are distinct - left hand and right hand

"what is the probability that a matched set (i.e., a left- and right-hand glove of the same color)"

A matched set needs to have a left and right hand glove of the same color. That is the only requirement. So all three left hand blue gloves are identical and all three right hand blue gloves are identical. Same for the green gloves.
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Karishma
Veritas Prep | GMAT Instructor
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Senior Manager
Joined: 02 Apr 2014
Posts: 485
GMAT 1: 700 Q50 V34
A box contains three pairs of blue gloves and two pairs of [#permalink]

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07 Oct 2017, 04:47
I solved this problem like this,

case 1: 1 Blue Left, 1 Blue right, any green color glove
Probability = (3c1(1 out of 3 blue left) * 3c1 (1 out of 3 blue right) * 4c1(1 out of 4 green gloves)/(10c3) = (3 * 3 * 4)/10c3 = 36/10c3

case 2: 1 Green Left, 1 Green right, any blue color glove
Probability = (2c1 * 2c1 * 6c1)/10c3 = (2 * 2 * 6)/10c3 = 24/10c3

case 3: 2 Blue Left, 1 Blue right OR 1 Blue Left, 2 Blue right
Probability = (3c2 * 3c1)/10c3 + (3c1 * 3c2)/10c3 = (2 * 3 * 3)/10c3 = 18/10c3

case 4: 2 Green Left 1 Green right OR 1 Green Left 2 Green right
Probability = ( 2c2 * 2c1)/10c3 + (2c1 * 2c2)/10c3 = (2 * 1 * 2)/10c3 = 4/10c3

In all above cases, we get a pair of left-right glove of same color.

So Total probability = sum of all above cases = (36 + 24 + 18 + 4)/10c3 = 41/60
Intern
Joined: 28 Apr 2015
Posts: 6
Re: A box contains three pairs of blue gloves and two pairs of [#permalink]

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08 Apr 2018, 19:49
arps wrote:
A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

(A) 3/10
(B) 23/60
(C) 7/12
(D) 41/60
(E) 5/6

Gloves:
LB = left blue
RB = right blue
LG = left green
RG = right green

LB: 3
RB: 3
LG: 2
RG: 2

Approach: 1 - P(no match)

No match situations:
P(LB, LB, LB): (3/10)(2/9)(1/8) = 1/120
P(RB, RB, RB): 1/120
P(LB, LB and a G): (3/10)(2/9)(4/8)*3 (for the 3 different ways we can pull the gloves) = 1/10
P(RB, RB and a G): 1/10 (same as above)
P(LG, LG, and a B): (2/10)(1/9)(6/8)*3 (for the 3 different ways we can pull the gloves) = 1/20
P(RG, RG, and a B): 1/20 (same as above)

P(no match) = 2(1/120) + 2(1/10) + 2(1/20) = 1/60 + 12/60 + 6/60 = 19/60

P(match) = 1 - P(no match) = 1 - 19/60 = 41/60
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Dan Morgan
MBA Wisdom
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Re: A box contains three pairs of blue gloves and two pairs of   [#permalink] 08 Apr 2018, 19:49

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