# Cambridge AS Levels Probability & Statistics 1 (Paper 5)

Unit S1: Probability & Statistics 1 (Paper 5)

*Updated for 2020 exams onwards*

Module 1 Representation of data (Part 1) - CIE S1 (135:35 mins)

Select a suitable way of presenting raw statistical data, and discuss advantages and/or disadvantages that particular representations may have.

Construct and interpret stem-and-leaf diagrams, box-and-whisker plots, histograms and cumulative frequency graphs.

Understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data.

Use a cumulative frequency graph to estimate the median value, the quartiles and the interquartile range of a set of data.

Calculate the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals such as Σx and Σx2, or Σ(x – a) and Σ(x – a)2.

Unit 1 Representation of data (Part 1) - Probability & Statistics (Paper 5) PDF
Unit 2 Representation of data (Part 1) - Probability & Statistics (Paper 5) Video
Module 2 Representation of data (Part 2) - CIE S1 (101:57 mins)

Representation of data (Part 2) - Cambridge AS Levels Probability & Statistics 1 (Paper 5) (101:57 mins)

Unit 1 Representation of data (Part 2) - Probability & Statistics (Paper 5) PDF
Unit 2 Representation of data (Part 2) - Probability & Statistics (Paper 5) Video
Module 3 Permutations and combinations - CIE S1 (115:20 mins)

Understand the terms permutation and combination, and solve simple problems involving selections.

Solve problems about arrangements of objects in a line, including those involving:
• repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’)
• restriction (e.g. the number of ways several people can stand in a line if 2 particular people must — or must not — stand next to each other).
Unit 1 Permutations and combinations - Probability & Statistics (Paper 5) PDF
Unit 2 Permutations and combinations - Probability & Statistics (Paper 5) Video
Module 4 Probability - CIE S1 (178:35 mins)

Evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g. for the total score when two fair dice are thrown), or by calculation using permutations or combinations.

Use addition and multiplication of probabilities, as appropriate, in simple cases.

Understand the meaning of exclusive and independent events, and calculate and use conditional probabilities in simple cases, e.g. situations that can be represented by means of a tree diagram.

Unit 1 Probability - Probability & Statistics (Paper 5) PDF
Unit 2 Probability - Probability & Statistics (Paper 5) Video
Module 5 Discrete random variables - CIE S1 (102:09 mins) *updated to 2020 Syllabus*
Construct a probability distribution table relating to a given situation involving a discrete random variable variable X, and calculate E(X) and Var(X).
Unit 1 Discrete random variables - Probability & Statistics (Paper 5) PDF
Unit 2 Discrete random variables - Probability & Statistics (Paper 5) Video
Module 6 Binomial distribution - CIE S1 (87:08 mins)

Use formulae for probabilities for the binomial distribution, and recognise practical situations where the binomial distribution is a suitable model (the notation B(n, p) is included).

Use formulae for the expectation and variance of the binomial distribution.

Unit 1 Binomial distribution - Probability & Statistics (Paper 5) PDF
Unit 2 Binomial distribution - Probability & Statistics (Paper 5) Video
Module 7 The normal distribution - CIE S1 (144:13 mins)

Understand the use of a normal distribution to model a continuous random variable, and use normal distribution tables.

Solve problems concerning a variable X, where X ~ N(μ, σ2), including
• finding the value of P(X > x1), or a related probability, given the values of x1, μ, σ,
• finding a relationship between x1, μ and σ given the value of P(X > x1) or a related probability.

Recall conditions under which the normal distribution can be used as an approximation to the binomial distribution (n large enough to ensure that np > 5 and nq > 5), and use this approximation, with a continuity correction, in solving problems.

Unit 1 The normal distribution - Probability & Statistics (Paper 5) PDF
Unit 2 The normal distribution - Probability & Statistics (Paper 5) Video

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