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! 🙂

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