Probability

Expert replies

prernamalhotra: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Apr 02, 2014 2:01 amFollowed by: 1 member; Thanked: 2 times

by prernamalhotra » Fri Jul 18, 2014 4:32 am

A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

1)1/144
2)1/143
3)1/24
4)1/23
5)1/12

Thank you,
Prerna

Like this post

Source: Beat The GMAT — Problem Solving | Fri Jul 18, 2014 4:32 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Jul 18, 2014 4:50 am

prernamalhotra wrote:A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

1)1/144
2)1/143
3)1/24
4)1/23
5)1/12

Since 12 pairs are dropped in the bag, the total number of gloves in the bag = 2*12 = 24.
The first glove chosen can be of any color.
We need to determine the probability that -- from the 23 REMAINING GLOVES in the bag -- the SECOND glove chosen is the mate of the first.
P(2nd glove matches the 1st) = 1/23.

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

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Jul 18, 2014 4:52 am

prernamalhotra wrote:A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

1)1/144
2)1/143
3)1/24
4)1/23
5)1/12

Alternate approach:

Number of ways to choose 2 gloves from 24 options = 24C2 = (24*23)/(2*1) = 12*23.
Number of matching pairs in the bag = 12.
P(matching pair is selected) = 12/(12*23) = 1/23.

The correct answer is D.

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jul 18, 2014 5:40 am

prernamalhotra wrote:A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

1)1/144
2)1/143
3)1/24
4)1/23
5)1/12

Probability = Favorable Outcomes/Total Outcomes

Favorable outcomes = 24 x 1
(The first glove can be chosen as any glove out of 24 pieces and second glove can be chosen in one way only because every piece has just one matching glove)

Total outcomes = 24 x 23
(The first glove can be chosen as any glove out of 24 pieces and second glove can be chosen as any glove out of remaining 23 pieces)

Therefore Probability = 24 x 1 / 24 x 23

Probability = 1/23

Answer : Option D

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Fri Jul 18, 2014 11:17 am

Hi prernamalhotra,

Certain probability questions that you might see on Test Day are more about "logic" skills than "math" skills.

When dealing with prompts such as this one, try putting yourself "in the situation" and talking through the logic:

Here we have 24 gloves in a bag (12 of each color). The question asks us to grab 2 gloves at random and asks for the probability that they're the same color. Notice how the prompt does NOT specify what the color has to be, so it can be any color as long as the two gloves match.

There's no way to know what the first glove would be, so it could be ANY of the 24 gloves. It's the second glove that MATTERS. After pulling the first glove, there's ONLY 1 glove left that matches (out of the 23 gloves remaining).

So, the probability is 1/23.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Jul 18, 2014 12:29 pm

prernamalhotra wrote:A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

A) 1/144
B) 1/143
C) 1/24
D) 1/23
E) 1/12

I used the same approach that Mitch used, but one of the great things about probability questions is that there are typically several approaches. Here's another.

Let's first find the probability of selecting a CERTAIN pair of gloves (e.g., 2 blue gloves).
So, P(2 blue gloves) = P(1st glove is blue AND 2nd glove is blue)
= P(1st glove is blue) x P(2nd glove is blue)
= (2/24) x (1/23)
= 2/(24)(23)
= 1/(12)(23)

IMPORTANT: Recognize that P(2 blue gloves) = P(2 green gloves) = P(2 red gloves) = P(2 brown gloves) etc.

Our goal is to find P(ANY matching pair), so...
P(ANY matching pair) = P(2 blue gloves OR 2 green gloves OR 2 red gloves OR 2 brown gloves....etc)
= P(2 blue gloves) + P(2 green gloves) + P(2 red gloves) + P(2 brown gloves) + ....
= 1/(12)(23) + 1/(12)(23) + 1/(12)(23) + 1/(12)(23) + ...(12 times)
= 1/(12)(23) times 12
= [spoiler]1/23 = D[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Jul 18, 2014 12:36 pm

A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

A) 1/144
B) 1/143
C) 1/24
D) 1/23
E) 1/12

Using the same colorful AND notation, my original approach would have been as follows:

P(matching pair) = P(select any glove as 1st glove AND select 2nd glove to match 1st)
= P(select any glove as 1st glove) x P(select 2nd glove to match 1st)
= (1) x (1/23) [since there are 23 gloves remaining and only 1 matches the 1st]
= [spoiler]1/23 = D[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

hi

by Scott@TargetTestPrep » Fri Jan 05, 2018 6:40 am

prernamalhotra wrote:A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

A)1/144
B)1/143
C)1/24
D)1/23
E)1/12

Let's say 2 of the 24 gloves are red. The probability of getting a red glove in the first selection is 2/24 and the probability of getting the matching red glove in the second selection is 1/23, for a total probability of:

2/24 x 1/23

Since there are 12 colors, there are 12 ways in which the same color can be selected. Thus, the probability of selecting two gloves of the same color is:

12 x 2/24 x 1/23 = 1/23

Alternate solution:

Since there are 12 colors and a pair of gloves in each color is in the bag, the bag has 24 gloves. We are asked to determine the probability that when two gloves are drawn, they are of the same color. Since the first glove can be any color, it doesn't matter what color it is. However, after the first glove is drawn, there is only one glove left out of the 23 remaining that can match the color of the first glove. Thus, the probability of two gloves of the same color is:

P(1st glove) x P(2nd glove) = 24/24 x 1/23 = 1/23

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review