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A bag consists of 56 marbles, each of which is either green, white, or

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Brant22
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A bag consists of 56 marbles, each of which is either green, white, or [#permalink] New post   14 Apr 2019, 23:02
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A bag consists of 56 marbles, each of which is either green, white, or red. If the probability of selecting a green marble is twice the probability of selecting a red marble, and the probability of selecting a white marble is twice the probability of selecting a green marble, how many red marbles are in the bag?

(A) 7
(B) 8
(C) 14
(D) 16
(E) 28
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B
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Re: A bag consists of 56 marbles, each of which is either green, white, or [#permalink] New post   14 Apr 2019, 23:14
Since there are 56 marbles
So, g + w + r = 56
according to question,
g = 2r
w = 2g
we can substitute each of the equations
and solve for g and find g= 16
Now solve for the number of red marbles:
16 = 2r
r =8
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Re: A bag consists of 56 marbles, each of which is either green, white, or [#permalink] New post   15 Apr 2019, 00:32
Ratio of G:R is 2:1
Ratio of W:G is 4:1

the ratio of R:W:R:Total is 2:4:1:7
if total is 56, so R = 8, which is Answer B
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Re: A bag consists of 56 marbles, each of which is either green, white, or [#permalink] New post   15 Apr 2019, 06:20
let probability of selecting a red marble be x/56
then probability of selecting a green marble becomes 2x/56
and probability of selecting a white marble will be 4x/56
as we know sum of their prob will be 1
i.e x/56+2x/56+4x/56 = 1
7x/56=1
x=8
so,probability of selecting a red marble is 8
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Re: A bag consists of 56 marbles, each of which is either green, white, or [#permalink] New post   16 Apr 2019, 17:46
Expert Reply
Brant22 wrote:
A bag consists of 56 marbles, each of which is either green, white, or red. If the probability of selecting a green marble is twice the probability of selecting a red marble, and the probability of selecting a white marble is twice the probability of selecting a green marble, how many red marbles are in the bag?

(A) 7
(B) 8
(C) 14
(D) 16
(E) 28



Notice that when the probability of choosing one kind of marble is twice the probability of choosing another kind of marble, it means that the number of marbles with the greater probability is twice the number of the other kind of marble. If we let the number of red marbles = r, then the number of green marbles = 2r and the number of white marbles = 4r.

Thus:

r + 2r + 4r = 56

7r = 56

r = 8

Answer: B
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Re: A bag consists of 56 marbles, each of which is either green, white, or [#permalink]
16 Apr 2019, 17:46
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