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3 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2 · Question 3(c)(iii)

Machines A and B produce 30% and 70% of a factory's output respectively. Machine A produces 4% defective products and machine B produces 3% defective products.

Given that a randomly selected item is defective, determine the probability that it was produced by machine A.

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Other parts of this question

  1. 3(a)(i)Calculate P(A ∪ B).[2 marks]
  2. 3(a)(ii)Determine P(A | B).[2 marks]
  3. 3(b)(i)Calculate P(G ∩ H).[2 marks]
  4. 3(b)(ii)Calculate P(G ∪ H).[2 marks]
  5. 3(c)(i)Show this information on a well-labelled tree diagram.[4 marks]
  6. 3(c)(ii)Calculate the probability that a randomly selected article is defective.[3 marks]
  7. 3(d)(i)Calculate the value of k.[2 marks]
  8. 3(d)(ii)Calculate the number of overtime hours that attendants will be expected to work each week.[3 marks]
  9. 3(d)(iii)Calculate the probability that an attendant will work less than 8 hours overtime in any week.[2 marks]

More practice: the rest of this paper · more Probability Theory questions · all CAPE Applied Mathematics Unit 1 past papers