Probability & Statistics 1 (for Paper 5): past paper questions

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• Question 1May/June 2026, paper 51Structured6 marks

  A fair red 4-sided spinner has sides numbered 1, 2, 3, 3. A fair blue 4-sided spinner has sides numbered $-2$, $-1$, $-1$, 1. The two spinners are spun and the numbers on the sides on which they land are noted.

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• Question 1Oct/Nov 2025, paper 51Structured6 marks

  The random variable $X$ takes the value $x$ with probability $k{x}^2$, where $k$ is a constant and $x$ takes the values $-2,1,2,3$ only. Draw up the probability distribution table for $X$, giving the probabilities as numerical fractions.

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• Question 1Oct/Nov 2024, paper 51Structured4 marks

  Nicola throws an ordinary fair six-sided dice. The random variable $X$ is the number of throws that she takes to obtain a 6. Find $\mathrm{P}(X<8)$.

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• Question 1Oct/Nov 2023, paper 51Structured4 marksHas a diagram

  The times taken by 120 children to complete a particular puzzle are represented in the cumulative frequency graph.

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• Question 2May/June 2026, paper 51Structured5 marks

  At a certain college, each of the 150 students studies exactly one of Art, Business or Drama. The numbers of male and female students studying each of these subjects is given in the table.

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• Question 2Oct/Nov 2025, paper 51Structured4 marks

  A fair six-sided dice with faces labelled 1, 2, 3, 4, 5, 6 is thrown repeatedly until a 6 is obtained. Find the probability that a 6 is obtained for the first time on the 8th throw.

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• Question 2Oct/Nov 2024, paper 51Structured6 marks

  The random variable $X$ takes the values $-2,-1,0,2,3$. It is given that $\mathrm{P}(X=x)=k(x^2+2)$, where $k$ is a positive constant. Draw up the probability distribution table for $X$, giving the probabilities as numerical fractions.

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• Question 2Oct/Nov 2023, paper 51Structured7 marks

  Hazeem repeatedly throws two ordinary fair 6-sided dice at the same time. On each occasion, the score is the sum of the two numbers that she obtains. Find the probability that it takes exactly 5 throws of the two dice for Hazeem to obtain a score of 8 or more.

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• Question 3May/June 2026, paper 51Structured9 marks

  Aldeny and Farnlee are two ski resorts. The table shows the number of centimetres of snow that fell each week for the first 15 weeks of last year.

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• Question 3Oct/Nov 2025, paper 51Structured8 marks

  The back-to-back stem-and-leaf diagram shows the annual salaries, in dollars, of 27 employees at each of two companies, Browns and Greens.

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• Question 3Oct/Nov 2024, paper 51Structured8 marks

  The time taken, in minutes, to walk to school was recorded for 200 pupils at a certain school. These times are summarised in the following table.

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• Question 3Oct/Nov 2023, paper 51Structured11 marks

  A farmer sells eggs. The weights, in grams, of the eggs can be modelled by a normal distribution with mean 80.5 and standard deviation 6.6. Eggs are classified as small, medium or large according to their weight.

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• Question 4May/June 2026, paper 51Structured8 marks

  Jong has a bag containing 5 red marbles and 7 blue marbles. He chooses marbles from the bag one at a time at random. Each time he replaces the marble in the bag.

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• Question 4Oct/Nov 2025, paper 51Structured5 marks

  Bag $A$ contains 8 red marbles and 3 blue marbles. Bag $B$ contains 4 red marbles and 1 blue marble. A marble is chosen at random from bag $A$.

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• Question 4Oct/Nov 2024, paper 51Structured6 marks

  Rahul has two bags, $X$ and $Y$. Bag $X$ contains 4 red marbles and 2 blue marbles. Bag $Y$ contains 3 red marbles and 4 blue marbles.

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• Question 4Oct/Nov 2023, paper 51Structured9 marks

  The times, to the nearest minute, of 150 athletes taking part in a charity run are recorded. The results are summarised in the table.

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• Question 5May/June 2026, paper 51Structured10 marks

  Three letters are chosen at random from the 9 letters in the word RETRIEVES. Find the probability that at least one of the letters is an E.

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• Question 5Oct/Nov 2025, paper 51Structured8 marks

  On any given day, Cooper either wears a blue jumper or he wears a green jumper or he does not wear a jumper. The probability that he wears a blue jumper is 0.6 and the probability that he wears a green jumper is 0.3.

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• Question 5Oct/Nov 2024, paper 51Structured9 marks

  The weights of the green apples sold by a shop are normally distributed with mean 90 grams and standard deviation 8 grams. Find the probability that a randomly chosen green apple weighs between 83 grams and 95 grams.

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• Question 5Oct/Nov 2023, paper 51Structured9 marks

  A red spinner has four sides labelled 1, 2, 3, 4. When the spinner is spun, the score is the number on the side on which it lands. The random variable $X$ denotes this score.

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• Question 6May/June 2026, paper 51Structured12 marks

  The heights of adult Indian elephants are normally distributed with mean $2.74\text{ m}$ and standard deviation $0.25\text{ m}$. A random sample of 250 of these elephants is chosen.

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• Question 6Oct/Nov 2025, paper 51Structured9 marks

  A factory produces chocolate bars. The weights of the bars are normally distributed with mean $155\text{ g}$ and standard deviation $6\text{ g}$. A random sample of 350 of these bars is chosen.

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• Question 6Oct/Nov 2024, paper 51Structured8 marks

  The heights of the female students at Breven college are normally distributed: • 90% of the female students have heights less than 182.7 cm. • 40% of the female students have heights less than 162.5 cm.

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• Question 6Oct/Nov 2023, paper 51Structured10 marksHas a diagram

  In a restaurant, the tables are rectangular. Each table seats four people: two along each of the longer sides of the table (see diagram). Eight friends have booked two tables, $X$ and $Y$.

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• Question 1May/June 2026, paper 52Structured6 marks

  A club has 15 members made up of 6 men and 9 women. Every Friday a team of 5 members is selected at random to represent the club in a competition. Find the probability that next Friday the team will consist of more men than women.

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• Question 7Oct/Nov 2025, paper 51Structured10 marks

  How many different arrangements are there of the 10 letters in the word SEYCHELLES?

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• Question 7Oct/Nov 2024, paper 51Structured9 marks

  How many different arrangements are there of the 9 letters in the word INTELLECT in which the two Ts are together?

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• Question 1Oct/Nov 2023, paper 52Structured5 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 distribution table for $X$ is shown below.

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• Question 2May/June 2026, paper 52Structured8 marks

  Ling has three coins. Each coin is biased so that the probability of obtaining a head is $\frac{1}{3}$. Ling throws all three coins at the same time.

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• Question 1Oct/Nov 2025, paper 52Structured3 marks

  A coin is biased so that the probability of obtaining a head when it is thrown is 0.4. The coin is thrown repeatedly until the first head is obtained. Find the probability that the first head is obtained on the 5th throw.

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