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Probability Challenge Question: Don’t Lose Your Marbles

ByChris Leleon July 14, 2014 , UPDATED ON April 14, 2015, inSAT

Probability strikes dread into almost everybody. Couple that with the fact that many probability questions are convoluted word problems so that even the most confident math-o-phile is quaking in her boots.

But before we get to the dread-inducing question a quick rundown.

The magical, make-your-life-a heck-of-a-lot-easier probability equation:

# of possibilities you are hoping to get # of total possibilities

Let’s take the formula out for a test drive.

I have a pouch with three red marbles and two blue marbles. What is the probability I grab a red marble?

The answer is 3 (since I’m hoping for the red marble when I dip my mitt into the pouch—and there are 3 red marbles).

The total number of marbles is 2 blue + 3 red = 5.

Therefore, the probability of grabbing a red marble is 3/5.

Now let’s make things slightly more complicated.

I have a pouch with 2 white marbles, 3 black marbles, and a blue marble. What is the probability I grab one white marble and then, without replacing the marble, grab a black marble?

Using the formula for the white marble, I get 2/6, since there are two white marbles (what I’m looking for) and six total marbles. Next, I want to apply the same math with the black marble, except I want to make sure that I remember there are now 5—and not 6—total marbles. So there are 3 black marbles out of a total 5, or 3/5.

Next, whenever I have separate events in probability, I want to multiply. The separate events in this case are 1) grabbing a white marble and 2) grabbing a black marble.

So I get 2/6, which can be reduced to 1/3 times 3/5: 1/3 x 3/5 = 1/5. If you are still with me, meaning you haven’t lost your marbles, you are ready for the challenge problem. Good luck!

A marble pouch contains 4 blue marbles, 6 brown marbles, and 3 golden marbles. What is the fewest number of brown marbles that I need to remove from the pouch to ensure that the odds of reaching in and grabbing a golden marble are greater than 50%?

0

1

3

4

6

After working through the problem, get a full explanation here:

Leave me any comments or questions you have below! 🙂

Chris Lele is the Principal Curriculum Manager (and vocabulary wizard) at Magoosh. Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including US News, GMAC, and Business Because. In his time at Magoosh, Chris has taught countless students how to tackle the GRE, GMAT, SAT, ACT, MCAT (CARS), and LSAT exams with confidence. Some of his students have even gone on to get near-perfect scores. You can find Chris on YouTube, LinkedIn, Twitter and Facebook!

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