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IB Mathematics: Applications and Interpretation HL · 13.1: Probability · 13.1.1

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Theoretical and experimental probability Problem set A

Give a probability as a fraction in its simplest form, or as a decimal when the numbers in the question are decimals. Show your working.

Difficulty: first skills applying them stretch

Skills

  1. A fair 10-sided die is numbered 1 to 10. It is rolled once. Find the probability that the score is

    1. (a) a factor of 12
    2. (b) greater than 7

  2. The probability that no goals are scored in a hockey match is 0.18. Find the probability that at least one goal is scored.

  3. A basketball player scores a free throw with probability 0.72. She takes 150 free throws. Find the expected number of scores.

  4. A random sample of 80 batteries is tested and 6 are faulty. Estimate the probability that a battery is faulty.

In context

  1. The 11 letters of the word MATHEMATICS are written on separate cards. One card is chosen at random. Find the probability that

    1. (a) the letter is M
    2. (b) the letter is a vowel

  2. In a random sample of 200 workers, 46 cycle to work. A town has 3500 workers.

    1. (a) Estimate the probability that a worker cycles to work.
    2. (b) Estimate how many of the town's workers cycle to work.

  3. A fair coin is tossed 4 times. Find the probability of at least one head.

Stretch

  1. A fair six-sided die is rolled 3 times. Find the probability of at least one six.

  2. A player wins a game with probability 0.18. The expected number of wins is 27. How many games does the player play?

jmaths.xyz · AI HL · 13.1.1 Theoretical and experimental probability