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SAT Math: What Are the Chances That Probability Drives You Nuts?

You can expect to see at least one probability question on the SAT. Probability measures the odds that something will happen, and it can be expressed as an equation: Probability = (number of times a certain event might occur) / (total number of events that might occur).

Some probability questions are fairly simple. For example: Let's say you have 6 balls and 2 are blue. If you randomly choose a ball, what is the chance it will be blue? (Answer: 1/3.)

But sometimes the SAT tosses out a probability question that's a little tricky. For example:The Apple store is selling iPods. They have iPod classics, blue iPod nanos, and orange iPod nanos. There are three times the number of iPod nanos as iPod classics. If one iPod is chosen at random from the store, the probability that an orange iPod nano will be chosen is two times the probability that a blue iPod nano will be chosen. If there are 16 orange iPod nanos in the store, what is the total number of iPods in the store?

(A) 20
(B) 24
(C) 32
(D) 40
(E) 48

Well, we have quite a lot of information here. We have three types of iPods, two of which are nanos. Let’s create a chart to organize our information.

So far, we know we have 16 orange iPod nanos. We need to figure out how many blue iPod nanos and how many classic iPods we have, so that we can find the total number of iPods. Where should we start?

The question tells us that if an iPod is chosen at random, the probability that an orange iPod nano will be chosen is two times the probability that a blue iPod nano will be chosen. This means there are two times as many orange nanos as there are blue nanos. (If there are two times as many orange nanos as blue nanos, it is twice as likely that one of the orange nanos will be chosen.)

So if we have 16 orange nanos, then we have 8 blue nanos—a total of 24 iPod nanos. Let’s add this information to our chart:

Now for the number of iPod classics. We can use our last piece of information: There are three times the number of iPod nanos as iPod classics. There are 24 nanos in total, so there are 8 classics. This comes out to 32 iPods at the Apple store.

Our answer is (C).

Let’s review some simple tips for probability questions:

• Remember your basic probability formula: Probability = (number of times a certain event might occur) / (total number of events that might occur)
• Organize your information. When you have a lot of information—such as 3 different types of items—the question will be clearer if you create a chart or table from the information.
• Know if your answer makes sense. This is key for any probability question. Make sure your answer fits with the scenario given in the question.

Need a full review on probability? Here you go. When you're ready, show your love for this probability quiz.

If you've got a math problem you can’t solve, drop it in the comments or email it to testpreptutor@sparknotes.com.

Related Post: Finding Your Lucky Number

By: Adam

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