4MA1/2FR Jun 2020, Question 14: Combined Events with Two-Way Tables

Part (a) · 2 marks

Fill in the missing cells of the table showing every possible total from adding spinner A and spinner B results.

1. 1Each score is the spinner A number plus the spinner B number.
2. 2Spinner A = 1: 1+1, 1+2, 1+3, 1+4 give 2, 3, 4, 5
3. 3Spinner A = 2: 2+1, 2+2, 2+3, 2+4 give 3, 4, 5, 6
4. 4Spinner A = 3: 3+1, 3+2, 3+3, 3+4 give 4, 5, 6, 7
5. 5So the table rows are A = 1: 2, 3, 4, 5; A = 2: 3, 4, 5, 6; A = 3: 4, 5, 6, 7

AnswerA = 1: 2, 3, 4, 5; A = 2: 3, 4, 5, 6; A = 3: 4, 5, 6, 7

Part (b) · 2 marks

Work out the probability that the combined score is 4 or less.

1. 1The table has 12 equally likely scores.
2. 2Row A = 1 gives scores 2, 3, 4, 5, so 2, 3, 4 are 4 or less (3 scores)
3. 3Row A = 2 gives scores 3, 4, 5, 6, so 3, 4 are 4 or less (2 scores)
4. 4Row A = 3 gives scores 4, 5, 6, 7, so 4 is 4 or less (1 score)
5. 53 + 2 + 1 = 6 scores are 4 or less
6. 6P(score is 4 or less) = 6/12

Answer6/12

Part (c) · 2 marks

Estimate how many of 84 paired spins give the same number on both spinners.

1. 1Find pairs where both spinners show same number: (1,1), (2,2), (3,3)
2. 2Count matching outcomes: 3
3. 3Probability = 3 / 12
4. 4Estimate = (3 / 12) × 84
5. 584 × 3 = 252
6. 6252 / 12 = 21

Answer21

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