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

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:

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