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4MA1/1H Jan 2023, Question 15: Tree Diagrams for Dependent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 7 marks

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The question, in short

From 9 cards (letters and numbers), two are drawn without replacement; complete a probability tree and find probabilities for both cards being numbers, and for one number and one letter.

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

Part (a) · 2 marks

Complete the two-stage probability tree for first and second card being number or letter, using the card counts.

  1. 1The 9 cards are A, 7, H, F, E, D, G, 5, C, so 2 have numbers and 7 have letters
  2. 2First card: P(number) = 2/9 and P(letter) = 7/9
  3. 3Tomas keeps the first card, so only 8 cards are left for the second card
  4. 4If the first card was a number: 1 number and 7 letters left, so P(number) = 1/8 and P(letter) = 7/8
  5. 5If the first card was a letter: 2 numbers and 6 letters left, so P(number) = 2/8 and P(letter) = 6/8

AnswerFirst card: 2/9 number, 7/9 letter. Second card: 1/8 number and 7/8 letter after a number; 2/8 number and 6/8 letter after a letter

Part (b) · 2 marks

Calculate the probability that both drawn cards show numbers.

  1. 1P(number then number) = P(first number) × P(second number | first was number)
  2. 2P(first number) = 2/9
  3. 3P(second number | first was number) = 1/8
  4. 4(2/9) × (1/8) = 2/72
  5. 52/72 = 1/36

Answer1/36

Part (c) · 3 marks

Calculate the probability that the two drawn cards consist of one number and one letter.

  1. 1P(one number and one letter) = P(number then letter) + P(letter then number)
  2. 2P(number then letter) = (2/9) × (7/8) = 14/72
  3. 3P(letter then number) = (7/9) × (2/8) = 14/72
  4. 4Total = 14/72 + 14/72 = 28/72
  5. 528/72 = 7/18

Answer7/18

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