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A box contains 3 red chips and 3 black chips. If chips are randomly re
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11 Apr 2022, 02:00
11 Apr 2022, 02:00
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Question Stats:
40% (03:07) correct
60% (03:15) wrong based on 5 sessions
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A box contains 3 red chips and 3 black chips. If chips are randomly removed from the box one at a time, without replacement, until all of the chips are removed, what is the probability that the last two chips are different colors?
A) 3/20
B) 3/10
C) 1/2
D) 3/5
E) 2/3
A) 3/20
B) 3/10
C) 1/2
D) 3/5
E) 2/3
Part of the project: GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Re: A box contains 3 red chips and 3 black chips. If chips are randomly re
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11 Apr 2022, 03:16
11 Apr 2022, 03:16
2
Quote:
A box contains 3 red chips and 3 black chips. If chips are randomly removed from the box one at a time, without replacement, until all of the chips are removed, what is the probability that the last two chips are different colors?
The last two chips are different colors means there are two possible cases:
Case 1: the last two chips could be a red and then a black
That means, there are 4 chips remaining 2 red and 2 black.
These can be picked in 4!/(2!*2!) ways = 6 ways
OR
Case 2: the last two chips could be black and then a red
That means, there are 4 chips remaining 2 red and 2 black.
These can be picked in 4!/(2!*2!) ways = 6 ways
Total number of ways in which the last two chips are different colors = 6 + 6 ways = 12 ways
Total Number of ways in which 6 chips (3 red chips and 3 black chips) can be removed = 6!/(3!*3!) = 20 ways
Required probability = 12/20 = 3/5
IMO D
General Discussion
Re: A box contains 3 red chips and 3 black chips. If chips are randomly re
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11 Apr 2022, 13:48
11 Apr 2022, 13:48
1
Well,
How many different ways you can pick up 3 red chips and 3 black chips?
Well, since you are using all 6 elements, 3 are red and 3 are black, it´s a typical case of permutation with repetition.
Therefore, the answer is 20 ways and this is the easy part.
(Easy if you recall that your math teacher asking how many words can you make with "MISSISSIPPI" ? - Yeah, it´s all about that).
The second part it´s harder which is how many ways ended with two different colors.
It´s like the license plate questions, but in this case is "permutation with repetition".
_ _ _ _ _ _
But, the last two you have to keep them as RED - RED or Black - Black.
So, it´s 4 elements with 2 red and 2 black.
How many different ways you can pick up 3 red chips and 3 black chips?
Well, since you are using all 6 elements, 3 are red and 3 are black, it´s a typical case of permutation with repetition.
Therefore, the answer is 20 ways and this is the easy part.
(Easy if you recall that your math teacher asking how many words can you make with "MISSISSIPPI" ? - Yeah, it´s all about that).
The second part it´s harder which is how many ways ended with two different colors.
It´s like the license plate questions, but in this case is "permutation with repetition".
_ _ _ _ _ _
But, the last two you have to keep them as RED - RED or Black - Black.
So, it´s 4 elements with 2 red and 2 black.
