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4 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2014 · Paper 2 · Question 3(a)(v)

60% of items are produced on Machine A and the rest on Machine B. Machine A produces 2% defectives and Machine B produces 1% defectives.

Two randomly selected items were tested. Calculate the probability that exactly one of them is defective.

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Other parts of this question

  1. 3(a)(i)Copy and complete the tree diagram by inserting the missing probabilities.[3 marks]
  2. 3(a)(ii)Calculate the probability that a randomly chosen item was produced by Machine A and is defective.[2 marks]
  3. 3(a)(iii)Show that the probability that a randomly chosen item is defective is 0.016.[3 marks]
  4. 3(a)(iv)Calculate the conditional probability that a randomly selected item came from Machine A given that it is defective.[3 marks]
  5. 3(b)(i)Calculate P(N).[2 marks]
  6. 3(b)(ii)Calculate P(N | M).[2 marks]
  7. 3(b)(iii)Calculate P(M ∩ N').[2 marks]
  8. 3(c)(i)State with a reason whether events M and N are mutually exclusive.[2 marks]
  9. 3(c)(ii)State with a reason whether events M and N are independent.[2 marks]

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