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A jar contains 6 red marbles and 9 blue marbles. If Evelyn

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A jar contains 6 red marbles and 9 blue marbles. If Evelyn

by swerve » Thu Oct 18, 2018 10:09 am

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A jar contains 6 red marbles and 9 blue marbles. If Evelyn reaches into the jar and simultaneously draws two marbles at random, what is the probability that she will draw two marbles of the same color?

A. 2/7
B. 12/35
C. 3/7
D. 17/35
E. 25/35

The OA is D

Source: Veritas Prep
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by Brent@GMATPrepNow » Thu Oct 18, 2018 10:18 am
swerve wrote:A jar contains 6 red marbles and 9 blue marbles. If Evelyn reaches into the jar and simultaneously draws two marbles at random, what is the probability that she will draw two marbles of the same color?

A. 2/7
B. 12/35
C. 3/7
D. 17/35
E. 25/35

The OA is D

Source: Veritas Prep
P(both are same color) = P(1st marble is red AND 2nd marble is red OR 1st marble is blue AND 2nd marble is blue)
= [P(1st marble is red) x P(2nd marble is red)] + [P(1st marble is blue) x P(2nd marble is blue)]
= [6/15 x 5/14] + [9/15 x 8/14]
= [2/5 x 5/14] + [3/5 x 8/14]
= 10/70 + 24/70
= 34/70
= 17/35

Answer: D

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Brent
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by fskilnik@GMATH » Thu Oct 18, 2018 11:51 am
swerve wrote:A jar contains 6 red marbles and 9 blue marbles. If Evelyn reaches into the jar and simultaneously draws two marbles at random, what is the probability that she will draw two marbles of the same color?

A. 2/7
B. 12/35
C. 3/7
D. 17/35
E. 25/35
Source: Veritas Prep
$$6R\,\,,\,\,9B$$
$$? = 1 - P\left( {\,{\rm{get}}\,1\,{\rm{red}},\,1\,{\rm{blue}}\,{\rm{in}}\,{\rm{2}}\,\,{\rm{simult}}{\rm{.}}\,{\rm{extractions}}\,} \right)$$
$$P\left( {\,{\rm{get}}\,1\,{\rm{red}},\,1\,{\rm{blue}}\,{\rm{in}}\,{\rm{2}}\,\,{\rm{simult}}{\rm{.}}\,{\rm{extractions}}\,} \right) = {{6 \cdot 9} \over {C\left( {6 + 9,2} \right)}} = \ldots = {{18} \over {35}}$$
$$? = {{35 - 18} \over {35}} = {{17} \over {35}}$$

This solution follows the notations and rationale taught in the GMATH method.

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Fabio.
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by Scott@TargetTestPrep » Thu Oct 25, 2018 5:07 pm
swerve wrote:A jar contains 6 red marbles and 9 blue marbles. If Evelyn reaches into the jar and simultaneously draws two marbles at random, what is the probability that she will draw two marbles of the same color?

A. 2/7
B. 12/35
C. 3/7
D. 17/35
E. 25/35

The probability of drawing two blue marbles is 9/15 x 8/14 = 3/5 x 4/7 = 12/35.

The probability of drawing two red marbles is 6/15 x 5/14 = 2/5 x 5/14 = 2/14 = 1/7 = 5/35.

So the total probability is 12/35 + 5/35 = 17/35.

Answer: D

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