BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

difficult level prob (gmat) plz help

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 96
Joined: Fri Apr 23, 2010 1:14 am
Thanked: 1 times
Followed by:1 members

difficult level prob (gmat) plz help

by quantskillsgmat » Fri Feb 24, 2012 10:08 pm
A box contains three pair of blue gloves and two pair of green gloves.Each pair consists of a left hand glove and right hand glove.Each of the glove is seprated from its mate and mixed together.If three gloves are randomly selected ,what is prob that a matched set(left and right glove of same color)will be there.
a)3/10 b)23/60 c)7/12 d)41/60 e)5/6
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 588
Joined: Sun Oct 16, 2011 9:42 am
Location: New Delhi, India
Thanked: 130 times
Followed by:9 members
GMAT Score:720

by rijul007 » Sat Feb 25, 2012 12:08 am
quantskillsgmat wrote:A box contains three pair of blue gloves and two pair of green gloves.Each pair consists of a left hand glove and right hand glove.Each of the glove is seprated from its mate and mixed together.If three gloves are randomly selected ,what is prob that a matched set(left and right glove of same color)will be there.
a)3/10 b)23/60 c)7/12 d)41/60 e)5/6

IMO D


kinds of combinations can be

B B B
G G G
B G G
G B B

I. All three are blue

Total number of combinations= 6C3 = 20
No of combinations in which no two of them are pairs = 2 (either all are left or all are right)
Hence, no of combinations such taht we get a atched set = 20-2 = 18

II. All are green

TOtal number of combinations = 4C3 = 4
No of combinations such that we get a matched set = 4 (there are 2 pairs of green in total, so each possible combination we give us a matching pair)


III. One blue, rest green

Total number of combinations = 6*4C2 = 36
we have two left gloves of green color and two right gloves of green color, number of combinations = 4

Number of combinations such that we get a matching set = 6*4 = 24


IV. one green, rest blue

Total number of combinations = 6C2*4 = 60
for blue,
3 left
3 right
number of combinations = 9

NUmber of combinations for a matching pait = 4*9 = 36



Combining the 4 cases,
Total number of combinations = 20+4+36+60 = 120
Total number of combinatiosn such taht we get a matching pair = 18+4+24+36 = 82

Probability = 82/120 = 41/60

Option D

I dont know if there is a shorter method to solve this...
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 406
Joined: Mon Jan 25, 2010 11:36 am
Location: Syracuse, NY
Thanked: 23 times
Followed by:4 members
GMAT Score:740

by tomada » Sat Feb 25, 2012 12:05 pm
I suppose that one way to save time would be to recognize that the total number of possible combinations = 10C3 = 10!/(7!)(3!) = 120.
I'm really old, but I'll never be too old to become more educated.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Feb 25, 2012 3:48 pm
quantskillsgmat wrote:A box contains three pair of blue gloves and two pair of green gloves.Each pair consists of a left hand glove and right hand glove.Each of the glove is seprated from its mate and mixed together.If three gloves are randomly selected ,what is prob that a matched set(left and right glove of same color)will be there.
a)3/10 b)23/60 c)7/12 d)41/60 e)5/6
Another approach:
P(matching set) = 1 - P(no matching set).

There are 3 ways to NOT select a matching set of gloves.

Case 1: 3 non-matching blue
P(1st glove is blue) = 6/10.
P(2nd glove is blue and for the same hand) = 2/9.
P(3rd glove is blue and for the same hand) = 1/8.
Since we want all of these events to happen, we multiply the fractions:
6/10 * 2/9 * 1/8 = 1/60.

Case 2: 1 green, 2 non-matching blue
P(1st glove is green) = 4/10.
P(2nd glove is blue) = 6/9.
P(3rd glove is blue and for the same hand as the 2nd glove) = 2/8.
Since we want all of these events to happen, we multiply the fractions:
4/10 * 6/9 * 2/8 = 4/60.
Since the one green glove could be 1st, 2nd or 3rd, we multiply by 3:
4/60 * 3 = 12/60.

Case 3: 1 blue, 2 non-matching green
P(1st glove is blue) = 6/10.
P(2nd glove is green) = 4/9.
P(3rd glove is green and for the same hand as the 2nd glove) = 1/8.
Since we want all of these events to happen, we multiply the fractions:
6/10 * 4/9 * 1/8 = 1/30.
Since the one blue glove could be 1st, 2nd or 3rd, we multiply by 3:
1/30 * 3 = 3/30 = 6/60.

Since any of the 3 cases above would yield no matching set of gloves, we add the probabilities:
P(no matching set) = 1/60 + 12/60 + 6/60 = 19/60.

Thus, P(matching set) = 1 - 19/60 = 41/60.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Fri Jan 06, 2012 9:52 am

by nikhilgupta » Mon Feb 27, 2012 9:57 pm
@GMATGuruNY

Doesn't the case 1 has a pair of 2 blue gloves. If we are taking 3 blue gloves then definitely we will have 1 pair
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Feb 28, 2012 4:08 am
nikhilgupta wrote:@GMATGuruNY

Doesn't the case 1 has a pair of 2 blue gloves. If we are taking 3 blue gloves then definitely we will have 1 pair
Here's Case 1:
Case 1: 3 non-matching blue
P(1st glove is blue) = 6/10.
P(2nd glove is blue and for the same hand) = 2/9.
P(3rd glove is blue and for the same hand) = 1/8.
Since we want all of these events to happen, we multiply the fractions:
6/10 * 2/9 * 1/8 = 1/60.
Note the words in red. Each glove selected is FOR THE SAME HAND: all three are for the left hand, or all three are for the right hand. Thus, no matching set -- one left and one right -- is selected.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1