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0580/42 Oct/Nov 2023, Question 8: Combined Events with Two-Way Tables

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

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The question, in short

Two fair dice with given faces: find probabilities and expectations for Dice A rolls, totals when both dice are rolled, and solve for n using a given probability.

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Part (ai) · 1 mark

Dice A has faces 1, 2, 2, 2, 3, 6. State the probability of rolling a 6.

  1. 1One 6 out of six faces: P(6) = 1/6

Answer1/6

Part (aii) · 1 mark

Dice A is rolled 150 times. Calculate the expected count of rolls landing on 6.

  1. 1150 × 1/6 = 25

Answer25

Part (bi) · 3 marks

Both dice are rolled once. Find the probability that the two results sum to 6.

  1. 1Totals of 6: (A = 2, B = 4) or (A = 3, B = 3)
  2. 2P = 3/6 × 3/6 + 1/6 × 2/6 = 9/36 + 2/36
  3. 3= 11/36

Answer11/36

Part (bii) · 2 marks

Given the two dice total 6, find the probability that both landed on 3.

  1. 1There are 6 × 6 = 36 equally likely outcomes.
  2. 2Total 6: A = 2 with B = 4 gives 3 × 3 = 9 ways
  3. 3Total 6: A = 3 with B = 3 gives 1 × 2 = 2 ways
  4. 4So 11 outcomes total 6, and 2 of them are both 3
  5. 5Probability = 2/11

Answer2/11

Part (c) · 2 marks

Dice B is rolled n times. Given the probability the nth roll is the first 3 is 32/729, find n.

  1. 1P(3) = 2/6 = 1/3, P(not 3) = 4/6 = 2/3
  2. 2(2/3)ⁿ⁻¹ × 1/3 = 32/729, so 2ⁿ⁻¹/3ⁿ = 2⁵/3⁶
  3. 3n = 6

Answer6

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Also searched as: 0580/42/O/N/23 · 0580_w23_qp_42 · 0580 w23 42 · question 8.
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