A-level · Probability

Conditional probability and tree diagramsExam-style questions

Using tree diagrams where the second-stage branches are conditional probabilities — multiplying along branches for P(A ∩ B), adding the paths to an event, and reversing the condition to find P(first | second).

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19 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A bag contains $3$ red and $2$ blue counters. Two are drawn at random without replacement. Find the probability that both are red.
Level 2 · 2 marksTry it
2
A bag contains $3$ red and $2$ blue counters. Two are drawn without replacement. Find the probability that the two counters are different colours.
Level 3 · 2 marksTry it
3
A bag contains $3$ red and $2$ blue counters. Two are drawn without replacement. Find the probability that both are blue.
Level 3 · 2 marksTry it
4
A bag contains $4$ red and $6$ blue counters. Two are drawn at random with replacement. Find the probability that both are red.
Level 3 · 2 marksTry it
5
A factory has two machines. Machine $A$ makes $60\%$ of items and $5\%$ of $A$ 's items are faulty; machine $B$ makes $40\%$ of items and $10\%$ of $B$ 's items are faulty. An item is found to be faulty. Find the probability it was made by machine $A$ .
Level 3 · 3 marksTry it

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