Quelpr
3 marksDiscrete Random Variables

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

A game requires rolling a six on a fair die to start.

Calculate the probability that at most 5 tosses are necessary to start the game.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 3(a)A random sample of 49 items with a sample mean of 13 is taken from a normal distribution with standard deviation 4. Calculate a 96% confidence interval for the…[3 marks]
  2. 3(b)(i)Determine the estimated linear regression equation y = a + bx for this data.[5 marks]
  3. 3(b)(ii)Estimate the width of a stem when the stem density is 8 using your regression equation.[2 marks]
  4. 3(b)(iii)The correlation coefficient is r = -0.63. Interpret this value in the context of the data.[2 marks]
  5. 3(c)(i)State appropriate null and alternative hypotheses to test for association between gender and rating of restroom facilities using a chi-squared test.[2 marks]
  6. 3(c)(ii)Determine the critical region for the chi-squared test at the 5% significance level.[2 marks]
  7. 3(c)(iii)Calculate the expected frequency corresponding to cell (row 2, column 2), which has an observed value of 24.[2 marks]
  8. 3(c)(iv)a)State whether you reject or fail to reject the null hypothesis.[1 mark]
  9. 3(c)(iv)b)Interpret the test decision in the context of the problem.[1 mark]
  10. 3(a)(i)Calculate the total number of distinct portfolios of 12 paintings that can be created.[3 marks]
  11. 3(a)(ii)Determine the number of portfolios that contain exactly 8 watercolours and 4 oil paintings.[4 marks]
  12. 3(a)(iii)Hence, calculate the probability that a randomly chosen portfolio contains 8 watercolours and 4 oil paintings.[2 marks]
  13. 3(b)(i)Calculate the probability that a player starts the game on the third toss of the die.[4 marks]
  14. 3(b)(iii)Determine the expected number of tosses required to start the game.[2 marks]
  15. 3(c)(i)Calculate the probability that exactly 4 faulty reports are received on Monday.[3 marks]
  16. 3(c)(ii)Calculate the probability that exactly 5 faulty reports are received over a five-day period.[4 marks]

More practice: the rest of this paper · more Discrete Random Variables questions · all CAPE Applied Mathematics Unit 2 past papers