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3 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2021 · Paper 2 · Question 3(a)(i)

Events A and B have probabilities P(A) = 1/4, P(A|B) = 5/8, and P(B|A) = 3/5.

Calculate P(A ∩ B).

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Other parts of this question

  1. 3(a)(ii)Calculate P(B).[3 marks]
  2. 3(a)(iii)Calculate P(A ∪ B).[2 marks]
  3. 3(a)(iv)State whether Event A and Event B are independent, giving ONE reason for your answer.[2 marks]
  4. 3(b)(i)Calculate the value of the constant b.[3 marks]
  5. 3(b)(ii)Determine the expected value of X, E(X).[3 marks]
  6. 3(b)(iii)Determine the variance of X, Var(X).[3 marks]
  7. 3(c)(i)Draw a probability tree diagram to represent the scenario.[4 marks]
  8. 3(c)(ii)Use the tree diagram to determine the probability that the counters drawn are of different colours.[2 marks]

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