Feb
24
2012

# GRE Probability Practice

When you’re flipping a coin to determine who takes the trash out, you usually aren’t thinking about probability. But, when you up the ante and decide to go for the best 2 out of 3, you really should be. Probability is an important consideration every time a coin is tossed or a die is rolled.

Let’s start out by looking at GRE coin problem:

A fair coin is to be tossed 5 times.

What is the probability that exactly 3 of the 5 tosses result in heads?

Remember the probability formula?

In order to apply the formula to this problem, the first thing we are going to do is determine the probability of any series of 5 tosses, which will also give the number of possible outcomes.

Here, there are 5 tosses, each with a probability of ½. Therefore, any one outcome of a series of 5 tosses will have the probability:

That number also tells us that a there are 32 possible outcomes for a series of 5 tosses.

In order to calculate the number of ways we can have exactly 3 heads in 5 tosses, we should use the combination formula, plugging 5 in for n and 3 in for k:

So, there are 10 ways we could get 3 exactly 3 heads in a series of 5 tosses and there are 32 possible outcomes in a series of 5 tosses. Putting those numbers together, we get:

Keep an eye out for one more blog entry in my probability series. In the meantime, let us know – have you seen probability questions on your GRE?

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#### About the Author: Paula Martin

Paula has taught for Kaplan since 2008. Her areas of expertise include GRE, GMAT and PCAT. She enjoys both the camaraderie of the classroom and the deeper relationship that is developed through tutoring. Paula loves to encourage and motivate her students. In 2001, Paula graduated from Emory University with a BS in Biology. Since then, she has lived in Honduras (where she taught English), worked as a researcher, served as a training and compliance coordinator, taught herself graphic design and explored the artistic outlets of painting and pottery. Paula plans to pursue a Certification in Biblical Storytelling in 2012 and to become a Master Biblical Storyteller by December 2013.

• Ari

Am I the only one that this doesn’t make sense to?? I don’t understand where you got 5*4*3*2*1/ (3*2*1*)(2*1). Can you explain the end in a little more detail? Thanks!!

Ari,

When you have a factorial (!), it tells you to multiply the number times every number below it, all the way to 1.

For example, 7 factorial (7!) is 7x6x5x4x3x2x1, whereas 5! is 5x4x3x2x1.

You may want to check out my post on combinations and permutations–it will explain that last formula more thoroughly: http://blog.kaplangradprep.com/2012/02/15/gre-combinations-and-permutations-basics/

Let me know if you have any additional questions!
Paula

• ShauntriceArt

gr8 post…math scares me. lol

• Paula Martin

Thank you, ShauntriceArt!

Don’t be scared! Practice, practice, practice…you’ll see that the same types of problems show up again and again on the GRE.

Best,
Paula

• Renita Vanderpuije

do u always have to use combination in find the numerator for such problems.

• Paula Martin

Renita,

If you’re looking for how many ways you can get heads or tails _ out of _ times, then combination is the best way to find the numerator.

As you practice, if you’ll pay attention to the explations for the problems you do, you’ll see that there are alternative versions of this problem that will not require combination.

All the best!
Paula