GRE Probability: A Roll of the Dice

April 9, 2012
Paula Martin

GRE blogWe’ve reviewed probability fundamentals here , here and here. Let’s look at one more probability example:

Each of 3 fair dice has sides numbered 1, 2, 3, 4, 5, and 6. If these 3 dice are all rolled at the same time, what is the probability that exactly 2 of these dice will show a 1?

For any one die, there is a 1/6 probability of rolling a 1. That also tells us that there is a 5/6 probability of rolling any other number.

Since we’re rolling 3 dice at once, and we want the probability that exactly 2 of them will show a 1, we can quickly figure out how many ways that can happen by jotting some notes down. We could roll 1 – 1 – x, or 1 – x – 1, or x – 1 – 1 (where x indicates any other number than 1.)

Any one of those outcomes represents exactly 2 dice showing a 1; therefore, there are 3 desired outcomes.

In order to determine the probability of one toss of the dice, we multiply the probability of the outcomes together. That means we have to multiply the probability of rolling a 1, times the probability or rolling a second 1, times the probability of rolling any other number:

This is where you have to really pay attention. One of the answer choices will very likely be 5/216.

However, that will not be the correct answer choice! You see, we just calculated the probability of rolling 1, 1, x. BUT, when we jotted down all of the outcomes that would give us exactly 2 dice showing a 1, there were two other possible outcomes. That means that we need to take the probability of 1, 1, x and multiply it times 3 to account for the probability of all three possible outcomes:

One of the keys to probability problems on the GRE is paying attention to exactly what you are solving for, and to what it is that you know at any given moment. Remember to always read the question one more time to make sure that the answer you select truly does answer the question at hand!

If you have questions about probability, ask them here.

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.

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