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There are 10 red and blue marbles in a box. If two marbles are random 06 Dec 2019, 06:07
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85% (hard)

Question Stats:

48% (02:25) correct 52% (02:20) wrong based on 190 sessions

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There are 10 red and blue marbles in a box. If two marbles are randomly taken out of the box, is the probability of picking two red marbles greater than 1/3?

1)The probability of getting both blue marbles is less than 2/3
2) There are more red marbles than blue marbles in the box.
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E
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There are 10 red and blue marbles in a box. If two marbles are random 08 Dec 2019, 08:13
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Abhi077
There are 10 red and blue marbles in a box. If two marbles are randomly taken out of the box, is the probability of picking two red marbles greater than 1/3?

1)The probability of getting both blue marbles is less than 2/3
2) There are more red marbles than blue marbles in the box.
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The be clear, is B not sufficient because, assuming 6 red balls ...
6/10* 5/9 = 1/3


but 7 red balls would be greater than 1/3
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There are 10 red and blue marbles in a box. If two marbles are random 09 Dec 2019, 19:45
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Abhi077
There are 10 red and blue marbles in a box. If two marbles are randomly taken out of the box, is the probability of picking two red marbles greater than 1/3?

1)The probability of getting both blue marbles is less than 2/3
2) There are more red marbles than blue marbles in the box.
Show more

Let the red balls be R, so we are looking for \(\frac{RC2}{10C2}>\frac{1}{3}.....\frac{R(R-1)}{90}>\frac{1}{3}...R(R-1)>30\) So, R>6

1)The probability of getting both blue marbles is less than 2/3
So \(\frac{BC2}{10C2}<\frac{2}{3}.....\frac{B(B-1)}{90}<\frac{2}{3}...B(B-1)<2*30\) So, B<9
If B=5, R=5..NO R is not >6
If B=2, R=8..YES
Insuff

2) There are more red marbles than blue marbles in the box.
If R=6..No
If R>6..Yes
Insuff

Combined
If R=6..No
If R>6..Yes
Insuff

E
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There are 10 red and blue marbles in a box. If two marbles are random 11 Dec 2019, 20:51
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chetan2u
Abhi077
There are 10 red and blue marbles in a box. If two marbles are randomly taken out of the box, is the probability of picking two red marbles greater than 1/3?

1)The probability of getting both blue marbles is less than 2/3
2) There are more red marbles than blue marbles in the box.

Let the red balls be R, so we are looking for \(\frac{RC2}{10C2}>\frac{1}{3}.....\frac{R(R-1)}{90}>\frac{1}{3}...R(R-1)>30\) So, R>6

1)The probability of getting both blue marbles is less than 2/3
So \(\frac{BC2}{10C2}>\frac{2}{3}.....\frac{B(B-1)}{45}>\frac{2}{3}...B(B-1)<30\) So, B<6
If B=5, R=5..NO R is not >6
If B=2, R=8..YES
Insuff

2) There are more red marbles than blue marbles in the box.
If R=6..No
If R>6..Yes
Insuff

Combined
If R=6..No
If R>6..Yes
Insuff

E
Show more
Should second not be
1)The probability of getting both blue marbles is less than 2/3
So \(\frac{BC2}{10C2}>\frac{2}{3}.....\frac{B(B-1)}{90}>\frac{2}{3}...B(B-1)<60\) So, B<8
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There are 10 red and blue marbles in a box. If two marbles are random 11 Dec 2019, 21:01
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globaldesi
chetan2u
Abhi077
There are 10 red and blue marbles in a box. If two marbles are randomly taken out of the box, is the probability of picking two red marbles greater than 1/3?

1)The probability of getting both blue marbles is less than 2/3
2) There are more red marbles than blue marbles in the box.

Let the red balls be R, so we are looking for \(\frac{RC2}{10C2}>\frac{1}{3}.....\frac{R(R-1)}{90}>\frac{1}{3}...R(R-1)>30\) So, R>6

1)The probability of getting both blue marbles is less than 2/3
So \(\frac{BC2}{10C2}>\frac{2}{3}.....\frac{B(B-1)}{45}>\frac{2}{3}...B(B-1)<30\) So, B<6
If B=5, R=5..NO R is not >6
If B=2, R=8..YES
Insuff

2) There are more red marbles than blue marbles in the box.
If R=6..No
If R>6..Yes
Insuff

Combined
If R=6..No
If R>6..Yes
Insuff

E
Should second not be
1)The probability of getting both blue marbles is less than 2/3
So \(\frac{BC2}{10C2}>\frac{2}{3}.....\frac{B(B-1)}{90}>\frac{2}{3}...B(B-1)<60\) So, B<8
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Thanks. Yes, it should be B(B-1)/10*9<2/3.....B(B-1)<60..B<9 as 8*7=56
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There are 10 red and blue marbles in a box. If two marbles are random 04 Sep 2024, 11:34
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