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4 marksCounting

CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 6(a)(iii)

Two fair coins and one fair die are tossed at the same time.

Calculate the probability of obtaining at least one head on the coins and an even number on the die on a particular attempt.

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Other parts of this question

  1. 6(a)(i)Calculate the number of outcomes in the sample space.[3 marks]
  2. 6(a)(ii)Find the probability of obtaining exactly one head.[2 marks]
  3. 6(b)Determine whether y = C_1 x + C_2 x^2 is a solution to the differential equation (x^2 / 2) y'' - x y' + y = 0, where C_1 and C_2 are constants.[6 marks]
  4. 6(c)(i)Show that the general solution to the differential equation 3(x^2 + x) dy/dx = 2y(1 + 2x) is y = C * ((x^2 + x)^2)^(1/3), where C in R.[7 marks]
  5. 6(c)(ii)Hence, given that y(1) = 1, solve 3(x^2 + x) dy/dx = 2y(1 + 2x).[3 marks]

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