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3 marksProbability Theory

CAPE Applied Mathematics Unit 1 · 2016 · Paper 2 · Question 3(a)(ii)

70% of people who use an antidepressant drug are women; 80% of women and 65% of men find it effective. A tree diagram is given with missing values x, y, and z.

Calculate the probability that the drug is effective.

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Other parts of this question

  1. 3(a)(i)Calculate the values of x, y and z.[3 marks]
  2. 3(a)(iii)Given that the drug was effective, what is the probability that a person using the drug is a man?[3 marks]
  3. 3(b)(i)Calculate the probability that a person selected at random pays for his/her item with cash.[2 marks]
  4. 3(b)(ii)Calculate the probability that a person selected at random makes a purchase that costs between 50 and 200.[2 marks]
  5. 3(b)(iii)Calculate the probability that a person selected at random makes a purchase over $200 and pays with a debit card.[2 marks]
  6. 3(b)(iv)Calculate the probability that a person selected at random uses a credit card, given that the purchase was under $50.[2 marks]
  7. 3(c)(i)Calculate P(R ∪ S).[2 marks]
  8. 3(c)(ii)Determine P(R|S).[2 marks]
  9. 3(c)(iii)State, with reason, whether R and S are mutually exclusive.[2 marks]
  10. 3(c)(iv)State, with reason, whether R and S are independent.[2 marks]

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