ACT Math: How to Solve Probability Problems

Chances are good that you’ve thought about probability before when playing games of chance. The higher the chances of coming out on top, the more likely you would be willing to play.

ACT Math Probability Problems -magoosh

For simple games, such as calling heads or tails on a coin flip, it’s easy to figure out what the chances are of winning. Physics and other variables aside, you have a 50% of getting it right.

When it comes to calculating more involved games, such as the chance of calling two or three coin flips correctly, then things get a bit more complicated. Sure, you could map out and think about every possibility, but that would cost you a lot of time.

What you need is a method for figuring out probability problems. However, it’s important to know that it’s not absolutely necessary to know a formal way to get the answer. The key here is to familiarize yourself with enough ACT-style questions so that you have a good idea of what to expect when you take the real test.

ACT Math: What is Probability?

In simple terms, probability is the likelihood of a particular event happening.

Probability = (favorable outcomes) / (total outcomes)

Therefore, a probability of 0 means that it will never happen. A probability of 1 means that it will always occur. Your answer will usually be somewhere between 0 and 1.

To find the probability of something not happening, simply subtract the probability from 1.

For Multiple Probabilities

To find the probability that two events will occur, multiply the probabilities together.

To find the probability of either event occurring, add the probabilities together.

ACT Math: Solving Probability Problems

The ACT Math section does not dive deep into probability concepts, so you’ll be fine knowing just the basics. Take a look at the example problem below for some practice:

A bag contains 2 purple marbles, 5 black marbles, and 5 blue marbles. You choose two marbles out of the bag at random. After the first marble is chosen, it is not replaced in the bag. What is the probability of choosing two purple marbles?

A. 1/66
B. 1/6
C. 1/36
D. 1/16
E. 1/26

Okay, there’s a lot of things going on here, so let’s break it down.

1. First of all, let’s take stock of how many purple marbles and total marbles we have here.

We have 2 purple marbles, and
2+5+5 = 12 marbles total.

The probability of choosing the first purple marble is 2/12.

2. Now let’s figure out the value of our second probability.

Since the first marble does not go back into the bag once it is chosen, we only have 11 marbles total for the second draw.

Whether or not we draw a purple marble the second time around only matters if we chose a purple marble the first time. What this means is that in order to figure out our second probability, we should assume that we picked a purple marble on our first draw.

Therefore, our second probability comes out to be 1/11.

3. Since the problem is asking for the probability of drawing two purple marbles, we need to multiply the two values together.

(2/12) * (1/11) = 2/132

All we need to do now is simplify, and our answer is A.


  • Minh Nguyen

    Minh's passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he's helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he's not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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