4024/12 May/Jun 2023, Question 23: Tree Diagrams for Dependent Events
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
From a 10-card set with shapes coloured green or red as tabulated, work out two probabilities: one for two green picks with replacement, one for matching shapes without replacement.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Ken draws twice, replacing each card; find the probability both show green.
- 1Green cards: 3 + 4 = 7, so P(green) = 7/10
- 2P(both green) = 7/10 × 7/10 = 49/100
Answer49/100
Part (b) · 3 marks
Irina draws two cards without replacement; find the probability both show the same shape.
- 1Squares: 4, triangles: 6
- 2P(both squares) = 4/10 × 3/9 = 12/90
- 3P(both triangles) = 6/10 × 5/9 = 30/90
- 4P(same shape) = 12/90 + 30/90 = 42/90
Answer42/90
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 LemmaraMore past-paper questions on tree diagrams for dependent events
Also searched as: 4024/12/M/J/23 · 4024_s23_qp_12 · 4024 s23 12 · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.