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:

 Not so bad, huh?

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?