A certain ski shop sells pairs of gloves in 12 different colors

Question

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?

1/144
1/143
1/24
1/23
1/12

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

Bunuel · Accepted Answer

We have 2*12 = 24 gloves on the floor. After we pick ANY, there are 23 left and there is only 1 matching pair left for the one we've already picked, so P = 1/23.

Answer: D.

Or: there are 12 matching pairs, and  C^2_{24}=23*12  ways to pick any two. P = (favorable)/(total) = 12/(23*12) = 1/23.

Answer: D.

Hope it's clear.

justbequiet · Answer

Chance of getting a color from the 12 different colored gloves =  \frac{24}{24} =1 
Chance of picking the same color as first sock out of the remaining  12*2-1=23  socks =  \frac{1}{23}

Probability of 1st x Probability of 2nd =  1*\frac{1}{23}=\frac{1}{23}

Answer is D

aadikamagic · Answer

Can someone please explain that does it make a difference to draw the gloves simultaneously and one by one.

Bunuel · Answer

Mathematically the probability of picking two gloves simultaneously, or picking them one at a time (without replacement) is the same.

klaster · Answer

is just me or does this question/answer make any logical sense?

'A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag...'  at this point there are 4 gloves in a bag 2 of each colour. Its irrelevant if there 200 pairs of colours being sold we only now care about what is in the bag - 4 gloves of 2 matching pairs

'...and a store clerk reaches in to draw two individual gloves'  So we are only dealing with what is in the bag. 4 gloves. The answer should be 1/3???

I know its a VeritasPrep question and not an OG so its not that important but am I losing my mind here?

chetan2u · Answer

hi,
there are 12 different colours so there are 12 pairs of gloves dropped..
first can be any of 24..so 24/24..
second has to be its pair, which will be just one out of remaining 23.. 1/23..
overall prob=24/24*1/23= 1/23..
hope it helped

klaster · Answer

*****

Hi Chetanu,

I'm not querying how they give or get their answer only that they are answering a different question.

There is no mention of   '...12 pairs of gloves dropped'   in the question. We are told:

' If one pair of each color is dropped '

To me the question is now saying ' given that we have now 4 gloves in a bag -   1 pair of each colour '

and a store clerk reaches in to draw two individual gloves (the store clerk is reaching into a bag of 4 gloves 2 pairs.) simultaneously and at random, what is the probability that she draws two gloves of the same color?

Is there any contesting that there are 4 gloves in bag and that they are 2 pairs? And that the clerk 'reaches in'? Then we are only dealing with 4 gloves of 2 pairs in the bag. The question is answering 24 gloves in a bag of 12 pairs.

I'd love Brunel's or a veritas expert to comment.

Got the GMAT on Tuesday so this is a welcome distraction

EMPOWERgmatRichC · Answer

Hi klaster,

The word "each" does NOT mean "two." Similarly, the phrase "each color" does NOT mean "two colors."

The first sentence in this prompt tells us that a shop sells gloves in 12 different colors. Next, we learn that "one pair" (meaning "two") of EACH COLOR (meaning the 12 colors that were previously mentioned) are dropped into a bag. This means that there are (2)(12) = 24 gloves in the bag.

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

cherryli2015 · Answer

picking up at the same time is considering picking up without replacement.

So no matter what color you pick for the first one, the probability is 1 
in order to match the first pcik, there are 23 left, there are at least 1 match to the first one
so the probability for 2nd pick is 1/23

the probability to pick 2 same color = 1* 1/23 = 1/23

Correct answer is D

Icecream87 · Answer

We have 12 pairs of gloves of different colours:
Probability of picking the first glove is 2/24
Probability of the second is 1/23

Since we can choose any colour, we multiply by the number of possibilities: 12

\frac{2}{24}*\frac{1}{23} *12 = \frac{1}{23}

keats · Answer

Can we do it this way too  Bunuel   Skywalker18 ?

Let us pick the two gloves that are different in color.
So, the # of cases will be 24 X 22 (pick any color first and then out of the remaining 22 gloves, pick any. This will ensure 2 gloves of different color)

So, probability of picking 2 different color gloves = (24x22)/(24 X 23) = 22/23

So, probability of not picking 2 gloves of same color = 1 - 22/23 = 1/23

Joc456 · Answer

I think the question prompt just wants to convey that the gloves are not returned when they are picked.

First glove--doesn't matter the color 
24/24 *23/24=1/23 D

keats · Answer

joannaecohen  What do you think about my approach to this question?

abhimahna · Answer

Yes, its another way to solve such questions.

keats · Answer

Thanks  abhimahna  for attending. Appreciate it, friend.

Joc456 · Answer

Keats   abhimahna  the way i wrote just makes sense. I suppose there are a lot of ways of doing it. I just figured 24/24*23/24 (ways 2 different color gloves can be picked) subtracted from one was the easiest

JeffTargetTestPrep · Answer

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

sahilvijay · Answer

select 1 pair from 12 pairs => 12C1
select 2 gloves from 24 gloves => 24C2

P= 12x2/24x23 => 1/23 ANSWER

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

D. With "pairs" probability questions, it's extremely important to recognize the difference between a specific pair (two red gloves, for example) and "any" pair (two gloves of the same color, in this case). Since here any pair will do, then it really doesn't matter which glove is selected first: there will then be 23 gloves left, and exactly one will match, so the probability is 1/23.

A certain ski shop sells pairs of gloves in 12 different colors

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A certain ski shop sells pairs of gloves in 12 different colors

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