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4MA1/2F Jan 2021, Question 9: Combined Events with Two-Way Tables

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 4 marks

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The question, in short

Grace uses a 3-sided spinner (6, 7, 8) and a 6-sided dice, subtracting the dice result from the spinner result to get a score. Complete the score table and find two probabilities.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Complete the table of all possible scores from subtracting each dice number from each spinner number; eight entries are already given.

  1. 1Each score is the spinner number take away the dice number.
  2. 2Spinner 7: 7 − 1 = 6, 7 − 2 = 5, 7 − 3 = 4, 7 − 4 = 3, 7 − 5 = 2, 7 − 6 = 1
  3. 3Spinner 8: 8 − 1 = 7, 8 − 2 = 6, 8 − 3 = 5, 8 − 4 = 4, 8 − 5 = 3, 8 − 6 = 2
  4. 4The completed table reads 5, 4, 3, 2, 1, 0 for spinner 6, then 6, 5, 4, 3, 2, 1 for spinner 7, then 7, 6, 5, 4, 3, 2 for spinner 8.

AnswerSpinner 6 row: 5, 4, 3, 2, 1, 0 (given); spinner 7 row: 6, 5, 4, 3, 2, 1; spinner 8 row: 7, 6, 5, 4, 3, 2

Part (b) · 1 mark

Find the probability that Grace's score is less than 6.

  1. 1The table has 3 × 6 = 18 equally likely outcomes.
  2. 2The scores that are not less than 6 are 6 (spinner 7, dice 1), 7 (spinner 8, dice 1) and 6 (spinner 8, dice 2), which is 3 outcomes.
  3. 3So 18 − 3 = 15 of the outcomes give a score less than 6.
  4. 4P(score less than 6) = 15/18 = 5/6

Answer15/18 (= 5/6)

Part (c) · 1 mark

Find the probability that Grace's score is an odd number.

  1. 1The odd scores in the table are 5, 3 and 1 in the spinner 6 row, 5, 3 and 1 in the spinner 7 row, and 7, 5 and 3 in the spinner 8 row.
  2. 2That is 3 + 3 + 3 = 9 odd scores out of the 18 outcomes.
  3. 3P(score is an odd number) = 9/18 = 1/2

Answer9/18 (= 1/2)

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