UniGeniusGCSE Maths · Edexcel 1MA1

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Algebraic probability and linked events

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Non-calculator · 3 marks

    (a) An experiment has exactly four possible outcomes A, B, C and D. Their probabilities are 2x, 3x, x + 0.1 and 0.3 respectively. Work out the probability of outcome B. (3)

  2. Question 2Non-calculator · 5 marks

    A bag contains nn sweets. 6 of them are orange. Two sweets are taken at random without replacement. The probability that both are orange is 13\frac{1}{3}.

    (a) Show that n2−n−90=0n^2 - n - 90 = 0. (3)

    (b) Work out the number of sweets in the bag. (2)

  3. Question 3Non-calculator · 3 marks

    (a) A bag contains n red counters and 4 blue counters, where n is greater than 4. Two counters are selected at random without replacement. The probability that the counters are different colours is 8/15. Work out n. You must show your working. (3)

Answers and marks

Question 1

(a) 0.3

  • P1 Establishing 2x+3x+x+0.1+0.3=12x+3x+x+0.1+0.3=1 or an equivalent valid method.
  • P1 Establishing 6x=0.66x=0.6 or an equivalent valid method.
  • A1 Correct answer: 0.3

Question 2

(a) 6n×5n−1=13\frac{6}{n} \times \frac{5}{n - 1} = \frac{1}{3} gives n2−n=90n^2 - n = 90.

  • P1 6n×5n−1\frac{6}{n} \times \frac{5}{n - 1}.
  • P1 Setting it equal to 13\frac{1}{3} and clearing the fractions.
  • A1 Reaching n2−n−90=0n^2 - n - 90 = 0 with every step shown.

(b) 10

  • M1 (n−10)(n+9)(n - 10)(n + 9) or the quadratic formula.
  • A1 Correct answer: 10.

Question 3

(a) 66

  • P1 Establishing 2n×4/((n+4)(n+3))=8/152n\times 4/((n+4)(n+3))=8/15 or an equivalent valid method.
  • P1 Establishing n2−8n+12=0n^{2}-8n+12=0 or an equivalent valid method.
  • A1 Correct answer: 66

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Algebraic probability and linked events

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