4MA1/1H Jan 2019, Question 20: Tree Diagrams for Dependent Events
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Bowl has n fruit, 4 oranges and rest apples; two are removed at random. Given probability that (n − 6) apples remain is 1/3, find n showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1The bowl has n − 4 apples, so n − 6 apples remain only if both fruits taken are apples
- 2P(two apples) = (n − 4)/n × (n − 5)/(n − 1) = 1/3
- 33(n − 4)(n − 5) = n(n − 1), so 3n² − 27n + 60 = n² − n
- 42n² − 26n + 60 = 0, so n² − 13n + 30 = 0 and (n − 10)(n − 3) = 0
- 5n = 3 is impossible (there are 4 oranges), so n = 10
Answer10
Stuck on a step? Read the free lesson: Tree Diagrams for Dependent Events
Practise more tree diagrams for dependent events questions
Real 4MA1 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: 4MA1 1H January 2019 · 4MA1/1H · 4ma1 jan19 1h · question 20.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.