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Probability · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SConditional probability and Bayes' theorem6 marksPaper 2~9 min
A factory produces electronic components using two machines, A and B. Machine A produces 60%60\% of the components and Machine B produces the remaining 40%40\%. Of the components produced by Machine A, 3%3\% are defective; of those produced by Machine B, 6%6\% are defective.
(a)
Draw a fully labelled tree to represent this information, showing all probabilities on each branch. [2 marks]
(b)
Calculate the probability that a randomly selected component is defective. [2 marks]
(c)
Given that a randomly selected component is defective, calculate the probability that it was produced by Machine A. [2 marks]
diagram

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