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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
1

Random variables

A takes specific numerical values, each with a probability. The distribution can be given as a table or as a function .

2

Probabilities sum to 1

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

All the probabilities total 1.
1.
Answer

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

3

Finding probabilities

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

1.
Answer

Formula recap

Probabilities sum to 1.
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.

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