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2.3 Probability

2.3 Probability

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Question 72

A microchip fabrication facility uses two distinct lithography processes: Machine α \alpha\,α and Machine β\betaβ. After processing, each component is classified as High Performance (HHH), Low Performance (LLL), or Defective (DDD).

The following information describes the distribution of these outcomes:

  • A component is processed by Machine α \alpha\,α with probability k k\,k or Machine β \beta\,β with probability 1−k1-k1−k.
  • For Machine α\alphaα, the probability of a Low Performance outcome is 0.25. No defects are produced by Machine α\alphaα.
  • For Machine β\betaβ, the probability of a High Performance outcome is mmm, 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)=0.21P(L) = 0.21P(L)=0.21:

a.

Find the value of kkk.

[3]
b.

Given also that the conditional probability P(β∣H)=449\displaystyle P(\beta | H) = \frac{4}{49}P(β∣H)=494​:

Find the value of mmm.

[4]
c.

Determine the probability that a randomly selected microchip is defective.

[2]
d.

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

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

[2]
Markscheme

2.3 Probability Questions

  1. A Level
  2. /Maths
  3. /2.3 Probability

200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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