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GRE Math — The Probability of a Coin Toss

If rate problems bring to mind moving trains, then there is no more iconic type of probability question than the coin toss. And there is good reason for this—coin tosses represent a fair portion of probability questions on the GRE. Even if a question doesn’t invoke the coin toss, the way we approach a coin toss problem can carry over to other types of probability questions.


An Easy GRE Probability Question

A fair-sided coin (which means no casino hanky-panky with the coin not coming up heads or tails 50% of the time) is tossed three times. What is the probability that I do not get two heads in a row?

The way to approach this problem is by drawing out the problem. What we want to find is the number of conditions that satisfy the above requirement.

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We can have one head in three different positions: HTT, TTH or THT.

We can also have two heads, but they cannot be consecutive, leaving us with HTH.

Were I to get all heads then that would break the restriction of not having at least two consecutive heads.

Finally, I can toss all tails: TTT.

So, in total I have five outcomes that satisfy the conditions in the question. We will call these the desired outcomes.

Once we’ve found this number, then what do we do?

With all probability questions, we always want to put the number of desired outcomes in the numerator. In the denominator, we want to put the total number of outcomes. The result of this fraction will give you the probability of an event happening.


To find the total outcomes, we will have to calculate how many different outcomes can result from three tosses of a coin. Without writing them all out, we can calculate this number by multiplying the total different outcomes for each toss. Because we can only get heads or tails, the number of different outcomes for each toss is 2.

Therefore the total number of different outcomes for three tosses is 2 x 2 x 2 = 8. Returning to the equation above, we get 5/8.

Not too bad? Well, that was a warm-up. The probability that you’ll run into more difficult coin toss questions is very high. So, study this example and get comfortable with the process you need to follow to come to a correct probability every time.

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