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Introduction to Probability · Ages 15–16

Classical Probability and Complements Practice

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For 10th-grade students. Verify that the outcomes are equally likely, identify the favorable outcomes, and calculate the probability. Simplify all fractions.

  1. You roll a fair six-sided die once. What is the probability of rolling an odd number?

  2. A standard deck contains 52 cards with 4 aces. What is the probability of drawing an ace at random?

  3. A box holds 20 raffle tickets numbered 1 through 20. What is the probability of drawing a ticket divisible by 5?

  4. Using the same box of 20 tickets numbered 1 through 20, what is the probability of drawing a ticket that is not divisible by 5?

  5. You spin a spinner divided into 8 equal sections numbered 1 to 8. What is the probability of landing on a number less than 3?

  6. A bag contains 5 green tiles, 3 blue tiles, and 2 yellow tiles. What is the probability of picking a tile that is not blue?

  7. A fair coin is tossed three times, giving 8 equally likely outcomes. What is the probability of getting at least one head?

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Classical Probability and Complements Practice

Answer key

  1. You roll a fair six-sided die once. What is the probability of rolling an odd number?

    3/6, which simplifies to 1/2 (the favorable outcomes are 1, 3, and 5).

  2. A standard deck contains 52 cards with 4 aces. What is the probability of drawing an ace at random?

    4/52, which simplifies to 1/13.

  3. A box holds 20 raffle tickets numbered 1 through 20. What is the probability of drawing a ticket divisible by 5?

    4/20, which simplifies to 1/5 (tickets 5, 10, 15, and 20).

  4. Using the same box of 20 tickets numbered 1 through 20, what is the probability of drawing a ticket that is not divisible by 5?

    1 - 1/5 = 4/5 (or 16/20 simplified to 4/5).

  5. You spin a spinner divided into 8 equal sections numbered 1 to 8. What is the probability of landing on a number less than 3?

    2/8, which simplifies to 1/4 (sections 1 and 2).

  6. A bag contains 5 green tiles, 3 blue tiles, and 2 yellow tiles. What is the probability of picking a tile that is not blue?

    7/10 (Total tiles = 10; non-blue tiles = 5 + 2 = 7, or 1 - 3/10 = 7/10).

  7. A fair coin is tossed three times, giving 8 equally likely outcomes. What is the probability of getting at least one head?

    7/8 (The complement is TTT, which has probability 1/8. 1 - 1/8 = 7/8).