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
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…
Answer this question and get it marked →May–June 2025, Paper 55
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…
Answer this question and get it marked →May–June 2024, Paper 52
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…
Answer this question and get it marked →May–June 2024, Paper 53
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…
Answer this question and get it marked →October–November 2024, Paper 51
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,…
Answer this question and get it marked →October–November 2024, Paper 52
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…
Answer this question and get it marked →October–November 2024, Paper 53
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…
Answer this question and get it marked →May–June 2023, Paper 52
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…
Answer this question and get it marked →May–June 2023, Paper 53
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…
Answer this question and get it marked →October–November 2023, Paper 52
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…
Answer this question and get it marked →October–November 2023, Paper 53
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 =…
Answer this question and get it marked →Other AS & A Level Mathematics topics
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