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IB Mathematics: Applications and Interpretation SL · 13.2: Probability Distributions · 13.2.1

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Discrete random variables and distribution tables Problem set B

Show the working. Write each distribution as a table and check that the probabilities add to 1. Give decimals exactly or to 3 significant figures.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. A drawing pin lands point up with probability 0.35. It is dropped twice. X is the number of times it lands point up.

    1. (a) Write the probability distribution of X as a table.
    2. (b) Find P(X ≥ 1).

  2. A wheel is split into 12 equal sectors numbered 1 to 12. It is spun once and X is the number it stops on.

    1. (a) Write down P(X = x) for each score.
    2. (b) Find P(X ≥ 10).
    3. (c) Find P(4 ≤ X ≤ 7).

  3. The table shows the probability distribution of X, the number of siblings of a student in a class.

    x01234P(X = x)0.220.38k0.090.05
    1. (a) Find the value of k.
    2. (b) Find P(X ≤ 1).
    3. (c) Find P(X ≥ 3).

  4. The probability that a train is late on any one day is 0.2. The days are independent. X is the number of late trains on a three-day trip.

    1. (a) Write the probability distribution of X as a table.
    2. (b) Find P(X ≥ 2).

In context

  1. A teacher chooses 2 students at random from a group of 3 boys and 6 girls. X is the number of boys chosen.

    1. (a) Write the probability distribution of X as a table.
    2. (b) Find P(X ≥ 1).

  2. Three cards are drawn one at a time, with replacement, from ten cards numbered 1 to 10. X is the number of times the card showing 10 is drawn.

    1. (a) Write the probability distribution of X as a table.
    2. (b) Find P(X ≥ 1).

  3. The table shows the probability distribution of R, the number of puncture repairs a cycle shop does in a day.

    r01234 or moreP(R = r)0.210.330.240.13k
    1. (a) Find the value of k.
    2. (b) Find P(R ≥ 2).
    3. (c) Find P(R ≥ 3 | R ≥ 2).

Stretch

  1. A discrete random variable X has the distribution shown, where k is a constant.

    x1234P(X = x)k²k2k0.69
    1. (a) Show that k² + 3k − 0.31 = 0.
    2. (b) Use your calculator to solve this equation and state the value of k.
    3. (c) Find P(X ≥ 3).

  2. A team of 3 is chosen at random from 5 girls and 3 boys. X is the number of boys in the team.

    1. (a) Write the probability distribution of X as a table.
    2. (b) Find P(X ≥ 1).
    3. (c) Find P(X = 2 | X ≥ 1).

jmaths.xyz · AI SL · 13.2.1 Discrete random variables and distribution tables