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ACT Probability practice questions

Probability sits in the Statistics & Probability reporting category on the ACT Math section. Prep36 has 15 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

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What Probability covers on the ACT

Within this skill the Prep36 bank covers complement of an event, dependent events without replacement, simple probability of one event, probability from a table (mutually exclusive events), sum of two dice and equally likely outcomes.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 15 questions tagged here is 6 easier, 4 medium and 5 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 probability questions, with the reasoning

Question 1 easy

A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. If one marble is drawn at random, what is the probability that it is blue?

  1. A. 1/3
  2. B. 5/12 correct
  3. C. 7/12
  4. D. 5/7
Why: Count the total first: 4 + 5 + 3 = 12 marbles, and 5 are blue, so P(blue) = 5/12. The other three all mismatch the numerator and denominator: 1/3 uses 4/12 (red), 7/12 is the probability of NOT drawing blue, and 5/7 compares blue to non-blue, which is odds rather than probability. Tip: probability is always favorable outcomes over the TOTAL number of outcomes. Write the total down before you write the fraction.
Question 2 medium

Three fair coins are tossed at the same time. What is the probability that exactly 2 of the coins land heads up?

  1. A. 1/4
  2. B. 3/8 correct
  3. C. 1/2
  4. D. 7/8
Why: There are 2³ = 8 equally likely outcomes, and exactly 2 heads occurs in 3 of them: HHT, HTH, and THH, so the probability is 3/8. The choice 7/8 is the probability of at least 1 head, and 1/4 counts only 2 of the 8 outcomes, missing one of the three orders. Tip: for a small number of coins or dice, list the full outcome set rather than guessing which arrangements count.
Question 3 hard

A carnival game costs $2.00 to play. A player wins a $5.00 prize with probability 1/4 and wins nothing otherwise. What is the expected net gain or loss for a player who plays the game once?

  1. A. a loss of $0.75 correct
  2. B. a gain of $0.25
  3. C. a gain of $1.25
  4. D. a gain of $3.00
Why: The expected prize is (1/4)($5.00) + (3/4)($0.00) = $1.25, and the player pays $2.00 every time, so the expected net result is $1.25 − $2.00 = −$0.75, a loss of 75 cents. The choice of a $1.25 gain stops at the expected prize and never subtracts the cost, and the $3.00 figure uses the $5.00 prize minus the $2.00 cost as if a win were certain. Tip: for expected value, weight every outcome by its probability first, then subtract any cost that is paid regardless of outcome.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 15

The other 12 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

Open the Math bank

Frequently asked questions

How many ACT probability questions does Prep36 have?
15, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
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