GRE Probability

Updated December 20, 2009

The GRE Quantitative Section contains all sorts of Problem Solving questions. Some of them involve Probability.

What You Need to Know

There’s not a lot of probability involved in the GRE, so relax. Out of the 28 math questions, you’re unlikely to get more than 1 or at most 2 probability questions.

That said, if you want to make sure to get the top GRE score, it’s always worth going over the basics. So here’s what you need to know:

Probability

The basic definition of probability you should use here is that the probability of event A happening equals the number of possible outcomes that result in event A, divided by the number of total possible outcomes. For example, the probability of getting 3 when rolling a die is 1/6, because there are 6 faces and only 1 has a 3 on it.

A few good things to remember- if an event must happen, it’s probability is equal 1. For example, rolling a number between 1 and 6 on a regular die has a probability of 1. If an event can’t happen, it will have a probability of 0. For example, rolling a 32 with a regular die has probability 0.

Laws of Probability

The probability of A or B happening equals A+B , the sum of the probabilities. For example, rolling a 1 or a 2 will have a probability of 1/3.

The probability of A and B happening equals A * B . For example, the probability of getting a 6 on a die and tossing a coin to get heads is $\frac{1}{6} * \frac{1}{2} = \frac{1}{12}$ . See? Easy!

Examples!

I have 4 green balls and 4 red ones in a bag. If I draw 2 balls randomly, what’s the probability that they’re both red?

Answer: For the first draw, the probability is $\frac{4}{8}$ , or 1/2. For the second draw, the probability is now $\frac{3}{7}$ , because you took 1 green ball out. So in total, the probability equals $\frac{1}{2} * \frac{3}{7} = \frac{3}{14}$ .

I have two fair dice.
Column A: The probability of getting a sum of 7 when tossing both dice.
Column B: The probability of getting numbers that are divisible by 3 on both dice.

Answer: Column A is easy- there are 6 ways to toss a sum of 7: 1|6, 2|5, 3|4, 4|3, 5|2, 6|1. There are a total of 36 results from tossing two dice (it’s 1/6 times 1/6). So in total you get $\frac{6}{36} = \frac{1}{6}$ . For column B, you have 4 options : 3|6, 6|3, 3|3, 6|6, so the total probability is $\frac{4}{36} = \frac{1}{9}$ , which is smaller, so column A is bigger. Answer is A.

That’s all you really need for tackling GRE’s probability questions.

Practice Free GRE Questions!

Online GRE Practice Tests

Here are some practice GRE quantitative tests:

GRE Quantitative (10 questions), GRE Quantitative (10 questions), GRE Quantitative Practice (10 questions), GRE Quantitative Practice Test (10 questions), GRE Quantitative Questions (10 questions), GRE Quantitative Comparison (10 questions) GRE Quadratic Equations (10 questions), GRE Algebra (9 questions) GRE Arithmetic Practice (10 questions), GRE Arithmetic (5 questions)

Learn More!

Check out the GRE Quantitative page for more information about the GRE’s quantitative section.

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