Probability and Combination Problems

Hi tbasebal24 and vsr2014,

The original post is over 2 years old and the response appears to be to a different question, but for anyone else who might be interested… here's how you can solve this problem.

In probability questions, you can either calculate what you "want" or what you "don't want"; certain probability questions are easier to deal with if you focus on what you "don't want" (since the two possibilities will always add up to 1).

Here, we have 3 red marbles and 7 blue marbles. We're told to select 2 marbles at random and we're asked for the probability that AT LEAST ONE will be blue. Instead of calculating all the different ways to get 1 or 2 blue marbles, let's calculate what we DON'T want: 0 blue marbles.

On the first pull, we'd have a 3/10 chance of NOT getting a blue marble. After pulling out that first marble….
On the second pull, we'd have a 2/9 chance of NOT getting a blue marble.

(3/10)(2/9) = 6/90 = 1/15 --> this is the probability of NOT getting what we want.

1 - 1/15 = 14/15 --> this is the probability of getting what we WANT.

Final Answer: D

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