Probability — Edexcel A-Level Statistics
Test yourself on Probability with PEARSON EDEXCEL A-Level practice questions.
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Probability explained
Tree diagrams, Venn diagrams and two-way tables are three ways to organise probabilities for combined events.
Read the full explanation
On a tree diagram, each branch shows a conditional probability; multiply along a path to get the probability of that sequence, and add the probabilities of all paths that satisfy the event. For two events A and B, P(A ∩ B) = P(A) × P(B | A). A Venn diagram shows events as regions inside a rectangle for the sample space; the overlap is A ∩ B, the union is everything inside either circle, and the outside region is neither event. A two-way table classifies outcomes by two categories; row and column totals give marginal probabilities, and a cell divided by a row or column total gives a conditional probability. Always check that probabilities on branches from one node sum to 1 and that all table cells sum to the grand total.
Your focus
- Construct a tree diagram, Venn diagram or two-way table from given probability information.
- Extract a required probability from each representation, including conditional probabilities.
- Check that branch probabilities, Venn regions or table totals are consistent and complete.
Probability exam tips
Marking Points
- Draws a tree diagram with correct branch probabilities, including conditional probabilities for the second event.
- Multiplies along a branch to find the probability of a combined outcome and adds across relevant branches for a total probability.
- Shades or identifies regions of a Venn diagram corresponding to A ∩ B, A ∪ B, A′ and neither A nor B.
- Reads probabilities from a Venn diagram, including the overlap and the region outside both events.
- Completes missing entries in a two-way table using row and column totals.
- Calculates marginal and conditional probabilities from a two-way table, e.g. P(A | B) = count in A ∩ B divided by count in B.
Examiner Tips
- 💡Label every branch of a tree diagram with its probability and check that branches from the same node sum to 1.
- 💡On a Venn diagram, write the overlap first, then fill the other regions by subtraction from the given totals.
- 💡For a two-way table, add row and column totals before answering so conditional probabilities use the correct denominator.
Common Mistakes
- Adding along a branch instead of multiplying: the error is summing probabilities along one path; the correction is to multiply along a path for a combined outcome and add across different paths.
- Using the wrong denominator for a conditional probability from a two-way table: the error is dividing by the grand total when the condition restricts the group; the correction is to divide by the total for the conditioning event.
- Forgetting the region outside both circles in a Venn diagram: the error is omitting outcomes in neither A nor B; the correction is to include the outside region when finding P(A′ ∩ B′) or checking totals.
- Assuming events are independent when drawing a tree diagram without replacement: the error is keeping the same second-branch probability; the correction is to update the denominator and numerator after the first outcome.