From a jar containing 4 red and 2 white marbles, Lionel draws two marb

Question

From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the probability that he picks one marble of each color?

A. 3/5
B. 8/15
C. 7/15
D. 2/5
E. 7/30

EMPOWERgmatRichC · Accepted Answer

Hi All,

In these types of Probability questions, there's usually several different ways that you can do the math. Many books will offer an explanation that focused on the Combination Formula, but this question can be solved with Permutations. While you should practice all of the methods, you should choose whichever is most comfortable (and fastest) for you on Test Day.

We're told that we have 4 red and 2 white marbles. We're asked for the probability of pulling two marbles that are DIFFERENT colors.

Even though the question states that the marbles are drawn simultaneously, we can still think of the marbles as "1st marble" and "2nd marble"; in this way, there are two acceptable "outcomes":

1) The 1st is red and the 2nd is white
2) The 1st is white and the 2nd is red

We can calculate the probability of each occurring:

1st red = 4/6
2nd white = 2/5
(4/6)(2/5) = 8/30 chance of this happening

1st white = 2/6
2nd red = 4/5
(2/6)(4/5) = 8/30 chance of this happening

8/30 + 8/30 = 16/30 = 8/15 chance of getting the result that we wanted.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

ans b 8/15...
 two ways ...
1) find prob of choosing each one... 4/6*2/5*2=8/15..
2) find prob of choosing of same colour... 4/6*3/5+2/6*1/5=7/15....
 so choosing one of each =1-7/15=8/15

buddyisraelgmat · Answer

Lionel draws two marbles simultaneously and at random. What is the probability that he picks one marble of each color?

Doesn't GMAT questions specifically mention  "with replacement" or "without replacement"

Is this question GMAT type?

WITH Replacement = 4/9
WITHOUT Replacement = 8/15

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: 8/15. There are two paths to one of each color: Red, then White; or White, then Red. So you’ll need to calculate the probability of each sequence and add them together.

Red, then White: There’s a 4/6 probability of drawing Red first, and then there will be 2 White left to draw from the remaining 5 marbles. So that’s a probability of 2/3 * 2/5 for a total of 4/15.

White, then Red: there’s a 2/6 probability of drawing White first, at which point there would be 4 Red left to draw from the remaining 5 marbles. That’s a probability of 1/3 * 4/5 = 4/15. Add together the two probabilities to get the total probability of one of each, and you get a total of 8/15.

BrentGMATPrepNow · Answer

P(one of each color) = P(1st is red   AND   2nd is white    OR    1st is white   AND   2nd is red)
= P(1st is red   AND   2nd is white)    +    P(1st is white   AND   2nd is red)
=   x   P(2nd is white)]    +      x   P(2nd is red)]
=   x   2/5]   +      x   4/5]
= 8/30   +    8/30
= 16/30
= 8/15

Answer: B

Cheers,
Brent

ScottTargetTestPrep · Answer

Solution:

The number of ways he can choose 2 marbles is 6C2 = (6 x 5)/2 = 15. The number of ways he can choose 1 marble of each color is 4C1 x 2C1 = 4 x 2 = 8. Therefore, the probability of picking one marble of each color is 8/15.

Alternate Solution:

Lionel can choose either R-W or W-R. The probability of R-W is 4/6 x 2/5 = 8/30 = 4/15, and the probability of W-R is 2/6 x 4/5 = 8/30 = 4/15. Thus, the probability of picking one marble of each color is 4/15 + 4/15 = 8/15.

Answer: B

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From a jar containing 4 red and 2 white marbles, Lionel draws two marb

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