Binomial distribution — Edexcel A-Level Statistics
Test yourself on Binomial distribution with PEARSON EDEXCEL A-Level practice questions.
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Binomial distribution explained
For a binomial distribution X ~ B(n, p), you must be able to find probabilities in two complementary ways.
Read the full explanation
The formula method uses P(X = r) = C(n, r) p^r (1 − p)^(n − r), where C(n, r) is the binomial coefficient, often written nCr. For example, if X ~ B(10, 0.3), then P(X = 4) = C(10, 4) × 0.3⁴ × 0.7⁶. The table method reads cumulative probabilities from binomial tables, usually giving P(X ≤ r) for given n and p. To find P(X = r) from tables, subtract consecutive cumulative values: P(X = r) = P(X ≤ r) − P(X ≤ r − 1). To find P(X ≥ r), use 1 − P(X ≤ r − 1). Always check whether the table gives P(X ≤ r) or P(X = r), and whether p is listed as a decimal or percentage. Recognise when a calculation is exact and when a table value is rounded.
Your focus
- Identify n and p from a binomial context and write X ~ B(n, p).
- Calculate P(X = r) using the binomial formula with correct substitution.
- Read cumulative binomial tables and convert between cumulative and exact probabilities using subtraction or complement rules.
Binomial distribution exam tips
Marking Points
- Correctly identifies the binomial parameters n and p from the context.
- Uses the formula P(X = r) = C(n, r) p^r (1 − p)^(n − r) with correct substitution.
- Uses cumulative binomial tables correctly, including reading the correct row and column.
- Converts between cumulative and exact probabilities using subtraction or 1 − P(X ≤ r − 1).
- Recognises the complement rule for P(X ≥ r) and P(X > r).
- Checks whether the table gives P(X ≤ r) or P(X = r) before using it.
Examiner Tips
- 💡Write down the distribution X ~ B(n, p) before calculating, so the parameters are clear.
- 💡When using tables, state the cumulative probability you are reading and show any subtraction or complement step.
- 💡Check whether the question asks for is related to the stated quantity , ≤, <, ≥ or > and adjust the table reading accordingly.
- 💡If a table value is rounded, say so and avoid over-claiming precision in the final answer.
Common Mistakes
- Misreading the table as giving P(X = r) when it gives P(X ≤ r). Correction: check the table heading and use subtraction to obtain exact probabilities.
- Using the wrong inequality direction, for example calculating P(X ≤ r) when P(X ≥ r) is required. Correction: use the complement rule 1 − P(X ≤ r − 1).
- Forgetting to subtract 1 from r when finding P(X ≥ r) from cumulative tables. Correction: P(X ≥ r) = 1 − P(X ≤ r − 1).
- Confusing n and p, or using p as a percentage without converting to a decimal. Correction: convert percentages to decimals before substitution.