Lemmara logoLemmaraWorked solution

4024/21 Oct/Nov 2023, Question 8: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using a frequency table for 40 children's monthly book counts, work out averages and a probability, then handle two book-selection scenarios with 7 fiction and 3 non-fiction books.

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

Part (ai) · 1 mark

State the most common number of books read.

  1. 1Highest frequency is 11, for 1 book
  2. 2Mode = 1

Answer1

Part (aii) · 1 mark

Determine the middle value of the 40 book counts.

  1. 1Median is between the 20th and 21st values
  2. 2Running totals 7, 18, 27: both are 2 books
  3. 3Median = 2

Answer2

Part (aiii) · 2 marks

Work out the average number of books read per child.

  1. 1Total books = 0 × 7 + 1 × 11 + 2 × 9 + 3 × 5 + 4 × 6 + 5 × 2 = 78
  2. 2Mean = 78 ÷ 40 = 1.95

Answer1.95

Part (aiv) · 2 marks

For a randomly picked child, give the simplified fraction chance of 4 or more books.

  1. 14 or more books: 6 + 2 = 8 children
  2. 2P = 8/40 = 1/5

Answer1/5

Part (bi) · 2 marks

With replacement after each pick, find the probability of getting one fiction and one non-fiction book.

  1. 1P(F then N) + P(N then F) = 2 × 7/10 × 3/10
  2. 2= 42/100 = 21/50

Answer21/50

Part (bii) · 3 marks

Taking 3 books without replacement, find the probability exactly one is fiction.

  1. 1P(F, N, N) = 7/10 × 3/9 × 2/8 = 42/720
  2. 2The fiction book can be 1st, 2nd or 3rd: 3 × 42/720
  3. 3= 126/720 = 7/40

Answer7/40

Stuck on a step? Read the free lesson: Tree Diagrams for Dependent Events

Practise more tree diagrams for dependent events questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on tree diagrams for dependent events

Also searched as: 4024/21/O/N/23 · 4024_w23_qp_21 · 4024 w23 21 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.