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A jar contains exactly 100 marbles; each marble contains exactly

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A jar contains exactly 100 marbles; each marble contains exactly  [#permalink]

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New post 14 Jul 2017, 22:03
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A jar contains exactly 100 marbles; each marble contains exactly 2 colors. Forty-three of the marbles are part-green and 21 of the marbles are part-red. If 3 marbles are to be selected at random, what is the probability that at least 2 of them contain no blue?

1.61 of the marbles are part-orange.
2.74 of the marbles are part-yellow
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Re: A jar contains exactly 100 marbles; each marble contains exactly  [#permalink]

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New post 15 Jul 2017, 02:23
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srikanth9502 wrote:
A jar contains exactly 100 marbles; each marble contains exactly 2 colors. Forty-three of the marbles are part-green and 21 of the marbles are part-red. If 3 marbles are to be selected at random, what is the probability that at least 2 of them contain no blue?

1.61 of the marbles are part-orange.
2.74 of the marbles are part-yellow


We know that their are 100*2 spaces to be filled with color
200 spaces

Now Green takes 43 spaces and Red takes 21 spaces = 64 spaces ; Leftover spaces 136

(1) says we have 61 spaces as orange-colored then too we will be left with 75 spaces with no further information (especially about blue)...Not sufficient

(2) says we have 74 spaces as yellow-colored then too we will be left with 62 spaces with no further information (especially about blue)...Not sufficient

On combining we have Green with 43 spaces, Red with 21 spaces, orange with 61 spaces and yellow with 74 spaces ...total 199 spaces have been occupied already. Hence only one space can takeup blue color, and hence
probability of atleast 2 of them contain blue will be 0 and hence
probability of atleast 2 of them contain no blue will be 1

C Sufficient
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Re: A jar contains exactly 100 marbles; each marble contains exactly  [#permalink]

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New post 21 Jun 2018, 16:10
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srikanth9502 wrote:
A jar contains exactly 100 marbles; each marble contains exactly 2 colors. Forty-three of the marbles are part-green and 21 of the marbles are part-red. If 3 marbles are to be selected at random, what is the probability that at least 2 of them contain no blue?

1.61 of the marbles are part-orange.
2.74 of the marbles are part-yellow


Alternate approach:

To calculate the probability of picking at least 2 marbles that contain no blue, we need to know how many of the 100 marbles are part-blue.
Question stem, rephrased:
How many of the 100 marbles are part-blue?

Total marbles = (total part-green) + (total part-red) + (total part-orange) + (total part-yellow) + (total part-blue) - (number of marbles that contain exactly two colors).

Total marbles = 100.
Total part-green = 43.
Total part-red = 21.
Since all of the marbles contain exactly 2 colors, the number of marbles that contain exactly two colors = 100.

Plugging these values into the equation above, we get:
100 = 43 + 21 + (total part-orange) + (total part-yellow) + (total part-blue) - 100
200 = 64 + (total part-orange) + (total part-yellow) + (total part-blue)
136 - (total part-orange) - (total part-yellow) = total part-blue
Total part-blue = 136 - (total part-orange) - (total part-yellow).

Statement 1: total part-orange = 61
Plugging this value into the blue equation above, we get:
Total part-blue = 136 - 61 - (total part-yellow).
Since the value in red is unknown, the number of part-blue marbles cannot be determined.
INSUFFICIENT.

Statement 2: total part-yellow = 74
Plugging this value into the blue equation above, we get:
Total part-blue = 136 - (total part-orange) - 74.
Since the value in red is unknown, the number of part-blue marbles cannot be determined.
INSUFFICIENT.

Statements combined: total part-orange = 61 and total part-yellow = 74
Plugging these values into the blue equation above, we get:
Total part-blue = 136 - 61 - 74 = 1.
SUFFICIENT.


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Re: A jar contains exactly 100 marbles; each marble contains exactly  [#permalink]

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Re: A jar contains exactly 100 marbles; each marble contains exactly   [#permalink] 23 Nov 2019, 21:06
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