Test Prep

# Improve Your Odds of a High Score with This ACT Probability Refresher

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Here's the coolest thing about improving your ability to answer statistics questions on the ACT: When we say that it'll improve the odds of you getting a high score, you'll know exactly what that means! Here how to break down two major types of probability questions.

## What Are the Odds?

Odds in the real world can be quite complicated, but on the ACT, they're one of the more straightforward calculations. It's just want/total: the number of outcomes that give you the result you want divided by the total number of possible outcomes. For example, let's say you would like to be chosen as the commencement speaker. If there are a total of five people being considered for the role, and only one will be selected, then there is one outcome that gives you what you want out of five total possibilities. Therefore, the probability is 1/5, or 20 percent. However, if you'd be happy if you or your BFF were selected, there are now two options that give you what you want out of five total possibilities, so the probability is now 2/5, or 40 percent. Where the ACT gets tricky is that it hides the want and total numbers in a long word problem or in a figure with a lot of other data in it. Organization is key here, so once you identify that the question is about probability, write down want/total and then find the numbers you need in the question. Always read carefully and use your pencil because there will be trap answers that contain numbers from the question that don't answer the question.

Also keep an eye out for questions that ask for the probability of something NOT happening. To calculate this, simply take 1 minus the probability of it happening. From the example above, we already determined there's a 2/5 or 40 percent chance that you or your BFF will be the commencement speaker. Therefore, our equation to determine the probability of neither of you being selected as speaker is 1-2/5, which equals 3/5, or 60 percent.

## Know What to Expect

One way that the ACT likes to make finding the odds more complicated is by asking you to do it more than once in a single problem. When looking for the expected value, you'll have to find the odds of several individual events, determine what each one is worth, and then add the results.

EXAMPLE: If a basketball player has a 60 percent chance of making a 2-point shot and a 30 percent chance of making a 3-point shot, what is the expected value from a player who makes two 2-point attempts and two 3-point attempts?

### Step 1 — List Out Each Event

The "events" in this case are the number of 2- and 3-point attempts.

2, 2, 3, 3

### Step 2 — Multiply Each Event by Its Probability

In this case, you've been given the odds, which is the percentage chance of a thing happening.

### Step 3 — Do the Math and Add Up the Values

Now that you have the correct number of events and their probabilities, it's time to solve.

= 1.2 + 1.2 + 0.9 + 0.9 = 4.2

ANSWER: The expected value for this scenario is 4.2.

Keep studying these terms and questions until you can quickly determine what to look for. Doing so is how the savviest students get what they want out of the total score of 36.

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