Conditional Probability

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A microchip fabrication facility uses two distinct lithography processes: Machine $\alpha\,$ and Machine $β\beta$ . After processing, each component is classified as High Performance ( $H$ ), Low Performance ( $L$ ), or Defective ( $D$ ).

The following information describes the distribution of these outcomes:

A component is processed by Machine $\alpha\,$ with probability $k\,$ or Machine $\beta\,$ with probability $1 - k$ .
For Machine $α\alpha$ , the probability of a Low Performance outcome is 0.25. No defects are produced by Machine $α\alpha$ .
For Machine $β\beta$ , the probability of a High Performance outcome is $m$ , and the probability of a Low Performance outcome is 0.15.

Given that the total probability of a component being classified as Low Performance is $P (L) = 0.21$ :

Find the value of $k$ .

[3]

Given also that the conditional probability $P(β∣H)=449\displaystyle P(\beta | H) = \frac{4}{49}$ :

Find the value of $m$ .

[4]

Determine the probability that a randomly selected microchip is defective.

[2]

Given that a specific microchip was found not to be defective:

Find the probability that it was processed by Machine $α\alpha$ .

[2]

Conditional Probability Questions

Practise Edexcel A Level Maths Conditional Probability with exam-style questions for A Level Maths. 100 questions covering Set Notation, Conditional Probability, Conditional Probabilities in Venn Diagrams, Probability Formulae, and Tree Diagrams, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.