Unit 4: Statistics and Probability
Topic 4.7: Discrete Random Variables Questions
Practice 8 exam-style questions for IB Math AA 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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2026• Aimnova practice — 4.7.1
A spinner pays out X dollars with P(X = 0) = 0.5, P(X = 2) = 0.3, P(X = 5) = 0.2. Find the expected payout.
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2026• Aimnova practice — 4.7.1
X has P(X = 1) = 0.2, P(X = 2) = 0.5, P(X = 3) = 0.3. Find E(X).
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2026• Aimnova practice — 4.7.1
In a game you pay $3 to roll a fair die. You receive $x equal to the number rolled. Find the expected gain per game, and state whether it is worth playing.
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2026• Aimnova practice — 4.7.1
A game gives a prize of $p with probability 0.2, otherwise the player loses $4. The game is fair. Find p.
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2026• Aimnova practice — 4.7.1
Two fair coins are tossed and X is the number of heads. Construct the distribution of X and find E(X).
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2026• Aimnova practice — 4.7.1
A discrete random variable X has P(X = x) = c(5 − x) for x = 1, 2, 3, 4. Find c.
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2026• Aimnova practice — 4.7.1
A distribution has P-values 0.1, 0.25, k, 0.2 and 0.15 for x = 0, 1, 2, 3, 4. Find k and P(X ≥ 3).
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2026• Aimnova practice — 4.7.1
A discrete random variable has P(X = x) = x/15 for x = 1, 2, 3, 4, 5. Verify it is a valid distribution and find E(X).
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