Discrete random variables — AS & A Level Mathematics (9709) questions by topic

Defining a random variable from two dice scores under a rule that changes depending on whether the scores match, finding unknown constants in a probability function from a given ratio condition, and building a probability distribution table for a biased dice's total score are typical of the 11 discrete random variables questions from 2023 to 2025, worth 3 to 8 marks.

Find, draw, construct and show lead the command words, with construct specifically asking for a full probability distribution table rather than a single value. Because a distribution table must sum to exactly one, submit your working for instant marking, so a missing outcome or a probability that does not total correctly is caught before the whole table is treated as finished.

May–June 2025, Paper 52

Question 1 · 3 marks

Rachel has three coins. The first coin is biased so that the probability of obtaining a head when it is thrown is 1/3. The second coin is biased so that the probability of…

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May–June 2025, Paper 55

Question 1 · 6 marks

Two fair 6-sided dice with faces labelled 1, 2, 3, 4, 5, 6 are thrown. The two scores are noted. The random variable X is defined as follows. - If the two scores are equal, X = 0…

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May–June 2024, Paper 52

Question 5 · 7 marks

Jasmine has one $5 coin, two $2 coins and two $1 coins. She selects two of these coins at random. The random variable X is the total value, in dollars, of these two coins. Show…

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May–June 2024, Paper 53

Question 1 · 8 marks

The numbers on the faces of a fair six-sided dice are 1, 2, 2, 3, 3, 3. The random variable X is the total score when the dice is rolled twice. Draw up the probability…

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October–November 2024, Paper 51

Question 2 · 6 marks

The random variable X takes the values −2, −1, 0, 2, 3. It is given that P(X = x) = k(x^2 + 2), where k is a positive constant. Draw up the probability distribution table for X,…

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October–November 2024, Paper 52

Question 3 · 6 marks

A fair coin and an ordinary fair six-sided dice are thrown at the same time. The random variable X is defined as follows. - If the coin shows a tail, X is twice the score on the…

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October–November 2024, Paper 53

Question 2 · 4 marks

A red fair six-sided dice has faces labelled 1, 1, 1, 2, 2, 2. A blue fair six-sided dice has faces labelled 1, 1, 2, 2, 3, 3. Both dice are thrown. The random variable X is the…

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May–June 2023, Paper 52

Question 1 · 6 marks

The random variable X takes the values -2, 2 and 3. It is given that P(X = x) = k(x^2 - 1), where k is a constant. Draw up the probability distribution table for X, giving the…

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May–June 2023, Paper 53

Question 3 · 7 marks

The random variable X takes the values 1, 2, 3, 4. It is given that P(X = x) = kx(x + a), where k and a are constants. Given that P(X = 4) = 3P(X = 2), find the value of a and the…

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October–November 2023, Paper 52

Question 1 · 5 marks

A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable X denotes the number of throws that exceed 30 metres. The probability…

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October–November 2023, Paper 53

Question 1 · 6 marks

Becky sometimes works in an office and sometimes works at home. The random variable X denotes the number of days that she works at home in any given week. It is given that P(X =…

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