ACT Practice Math Questions: Probability

By Lisa Zimmer Hatch, Scott A. Hatch

There’s a good chance that the ACT Math exam will contain one or more questions that deal with probability. There’s also a good chance that the odds of your answering those questions correctly will improve if you tackle the following practice questions.

Practice questions

  1. Sheila has 4 black socks and 2 navy socks in her laundry pile. If she randomly selects one sock from the pile, sets it aside, and then picks another sock from the pile, what is the chance that she will select the navy pair?


    The next question is based on the following information.

    The discard pile for a children’s card game contains 6 green cards, 8 yellow cards, 10 blue cards, and several red cards. There are no other cards in the discard pile. The probability of randomly choosing a yellow card from the pile is 1/4. Armando shuffles the discard pile and places the whole pile face down in front of the players to ready it for further play.

  2. To put a card into play, the players flip over the top card of the newly shuffled discard pile. What is the probability that the first player will flip over a green card?


Answers and explanations

  1. The correct answer is Choice (A).

    Before you find the chance Sheila will pick two navy socks, you first have to find the chance that the first sock she picks will be navy. That chance is 2/6 or 1/3 because 2 out of 6 socks are navy. Multiply that fraction by the probability that the second sock she chooses will also be navy. The second probability isn’t also 1/3 because Sheila has already picked a navy sock from the pile and set it aside. After she chooses the first navy sock, 5 socks remain in the pile and only 1 is navy. So the chance that the second sock she picks will be navy is actually 1/5. The chance that both socks Sheila picks will be a navy pair results from multiplying 1/3 by 1/5, which is 1/15. Pick Choice (A).

  2. The correct answer is Choice (A).

    First, you need to know the number of cards in the shuffled discard pile. If the discard pile contains 8 yellow cards and the probability of choosing a yellow card is 1 out of 4, there must be a total of 32 cards in the discard pile because


    is the same as


    The pile has a total of 6 green cards, so the probability that a green card is the top card is