Unit 4: Statistics and Probability
Topic 4.7: Discrete Probability Distributions Questions
Practice 20 exam-style questions for IB Math AI SL Topic 4.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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A discrete random variable X has P(X=1) = 0.2, P(X=2) = 0.5, P(X=3) = k. Find k.
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Find E(X) for the distribution P(X=0) = 0.4, P(X=1) = 0.4, P(X=2) = 0.2.
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State what E(X) represents in practical terms.
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A fair six-sided die is rolled. Find E(X), the expected score.
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A discrete random variable has P(X=2) = 0.3, P(X=4) = 0.5, P(X=6) = 0.2. Find P(X ≤ 4).
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A discrete random variable X has the probability distribution shown: P(X=1) = 0.1, P(X=2) = 0.3, P(X=3) = k, P(X=4) = 0.2.
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For a distribution with E(X) = 2.4, a game pays out X dollars and costs $2.40 to play. State whether the game is fair.
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A random variable X has Var(X) = 2.5.
(a) Find Var(4X − 3).
(b) The random variable Y is independent of X and has Var(Y) = 1.5. Find Var(X + Y) and the standard deviation of X + Y.
(a) Find Var(4X − 3).
(b) The random variable Y is independent of X and has Var(Y) = 1.5. Find Var(X + Y) and the standard deviation of X + Y.
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A game awards X points per turn. The distribution of X is P(X = 1) = 0.1, P(X = 2) = 0.3, P(X = 3) = 0.4, P(X = 4) = 0.2. Find E(X), and find the standard deviation of X, correct to three significant figures.
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The number X of faulty parts in a box of two is recorded. The distribution of X is P(X = 0) = 0.25, P(X = 1) = 0.5, P(X = 2) = 0.25. Find E(X), and find the standard deviation of X, correct to three significant figures.
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A spinner scores X points. The distribution of X is P(X = 2) = 0.2, P(X = 4) = k, P(X = 6) = 0.3, P(X = 8) = 0.1, where k is a constant. Find the value of k, find E(X), and find Var(X).
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The prize X, in dollars, from a raffle ticket is recorded. The distribution of X is P(X = 10) = 0.5, P(X = 20) = 0.3, P(X = 30) = 0.2. Find E(X), and find the standard deviation of X, correct to three significant figures.
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A spinner scores X with P(X=1) = 0.5, P(X=3) = 0.3, P(X=10) = 0.2. Find the expected score and explain why the spinner rarely shows the expected value.
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In a fairground game, a player spins a wheel and wins a prize X dollars. The distribution is P(X=0) = 0.5, P(X=1) = 0.3, P(X=5) = 0.2. It costs $2 to play.
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A raffle ticket has a net winning X dollars (a loss is negative). The distribution is:
x: −5, 10, w
P(X = x): 0.7, 0.25, 0.05
where w is the value of the top prize. The game is fair, so E(X) = 0. Find the value of the top prize w.
x: −5, 10, w
P(X = x): 0.7, 0.25, 0.05
where w is the value of the top prize. The game is fair, so E(X) = 0. Find the value of the top prize w.
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A discrete random variable X takes values 1, 2 and 3 with P(X=1) = 0.5, P(X=2) = 0.3, P(X=3) = 0.2. The experiment is performed twice independently.
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At a small bakery, the number of loaves X a customer buys has the distribution below.
x: 0, 1, 2, 3
P(X = x): 0.2, 0.5, 0.2, 0.1
x: 0, 1, 2, 3
P(X = x): 0.2, 0.5, 0.2, 0.1
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