S6.1StatisticsCore

Probability Distributions

A probability distribution lists every value a random variable can take alongside its probability. Because something must happen, all those probabilities add to 1 — the rule behind most distribution questions.

25 min Video by Zeeshan Zamurred Statistical Distributions

Edexcel AS Level Maths: 6.1 Probability DistributionsWatch the full walkthrough before the notes below.

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What you'll be able to do

Understand a discrete random variable
Read and build a probability distribution
Use the fact that probabilities sum to 1
Find a probability from the distribution

Random variables

A $discrete random variable$ $X$ takes specific numerical values, each with a probability. The distribution can be given as a table or as a function $P (X = x)$ .

Probabilities sum to 1

Every probability distribution must satisfy one rule: the probabilities of all possible values add up to $1$ . This lets you find a missing probability.

\sum P (X = x) = 1

All the probabilities total 1.

0.2 + 0.5 + k = 1

Answer

k = 0.3

Tip — A missing probability is found by making the whole distribution add to 1.

Finding probabilities

To find the probability of a range (e.g. $P (X \geq 2)$ ), add the probabilities of the relevant values. A distribution can also be defined by a formula, which you evaluate at each value.

P (2) + P (3) = 0.5 + 0.3

Answer

0.8

Formula recap

\sum P (X = x) = 1

Probabilities sum to 1.

P (X \geq a) = sum of relevant P (X = x)

Range probabilities.

Common mistakes to avoid

A distribution whose probabilities do not total 1.

Always check (or enforce) that the probabilities sum to 1.

Multiplying probabilities to find P(X ≥ 2).

Add the probabilities of the included values.

Key takeaways

A probability distribution pairs each value of X with its probability.
All probabilities sum to 1 (use this to find a missing one).
For a range, add the relevant probabilities.

Test yourself

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