ACT Math · Pre-Algebra
Elementary probability
Counting outcomes and computing simple probabilities.
What's tested in this subtopic
Items ask for the probability of a single event, of compound independent events, or for "at least one" using the complement rule.
Tactics that actually move your score
Probability is favorable outcomes over total outcomes. For "at least one" events, compute the probability of the complement (none) and subtract from 1. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy A bag contains 4 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Easy A bag contains 8 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Medium A bag contains 4 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Medium A bag contains 7 red marbles and 7 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Medium A bag contains 9 red marbles and 7 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Hard A bag contains 4 red marbles and 5 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Easy A bag contains 6 red marbles and 8 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Easy A bag contains 8 red marbles and 5 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Medium A bag contains 2 red marbles and 7 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Medium A bag contains 9 red marbles and 7 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Medium A bag contains 3 red marbles and 6 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Hard A bag contains 3 red marbles and 4 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Easy A bag contains 8 red marbles and 6 blue marbles. If one marble is drawn at random, what is the probability that it is red?
- Easy A bag contains 3 red marbles and 4 blue marbles. If one marble is drawn at random, what is the probability that it is red?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in ACT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.