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2 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2 · Question 3(b)(ii)

Events A and B have probabilities P(A) = 0.5, P(B) = 0.40, and P(A ∩ B) = 0.12.

State, with a statistical reason, whether events A and B are independent.

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Other parts of this question

  1. 3(a)(i)Determine the probability of selecting a green candle when one is chosen at random.[2 marks]
  2. 3(a)(ii)a)Three candles are randomly selected from the box. Using R for red and G for green, list the elements of the sample space.[2 marks]
  3. 3(a)(ii)b)Determine the probability that exactly two of the three candles selected are red.[3 marks]
  4. 3(b)(i)State, with a statistical reason, whether events A and B are mutually exclusive.[2 marks]
  5. 3(c)(i)Find the probability that a randomly chosen student studies neither French nor Spanish.[3 marks]
  6. 3(c)(ii)Find the probability that a randomly chosen student studies French only.[2 marks]
  7. 3(c)(iii)Find the probability that a student studies French given that they study Spanish.[2 marks]
  8. 3(d)(i)Show that X is a valid random variable.[2 marks]
  9. 3(d)(ii)Calculate the mean and standard deviation of X.[5 marks]

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