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 factory uses two machines, $A$ and $B$ , to make components. Machine $A$ makes $60\%$ of the components and machine $B$ makes the rest. Of the components made by machine $A$ , $3\%$ are defective; of those made by machine $B$ , $7\%$ are defective.

A component is chosen at random from the factory's output.
(a) Find the probability that it is defective. (3 marks)
(b) Given that it is defective, find the probability that it was made by machine $B$ . (2 marks)
(c) Two components are chosen at random. Find the probability that exactly one of them is defective. (2 marks)
Level 4 · 7 marksTry it