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
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prernamalhotra
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Since 12 pairs are dropped in the bag, the total number of gloves in the bag = 2*12 = 24.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
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.
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Alternate approach: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
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.
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GMATinsight
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Probability = Favorable Outcomes/Total Outcomesprernamalhotra 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
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
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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
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
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Brent@GMATPrepNow
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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.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 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
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Using the same colorful AND notation, my original approach would have been as follows: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
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
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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: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
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
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