Lemmara logoLemmaraWorked solution

0580/43 Oct/Nov 2021, Question 10: Tree Diagrams for Independent Events

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Work with a fair four-sided spinner showing 0, 1, 1, 3 and with Scott's two-part exam where theory pass is 0.9 and practical pass is 0.8; find the requested probabilities and n.

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

Part (ai) · 1 mark

State which of the numbers 0, 1, 1, 3 the spinner is most likely to show.

  1. 1Two of the four sections are numbered 1
  2. 2Most likely number = 1

Answer1

Part (aii) · 2 marks

For two independent spins, work out the probability of getting 1 on both.

  1. 1P(1) = 2/4 = 1/2
  2. 2P(1 both times) = 1/2 × 1/2 = 1/4

Answer1/4

Part (aiii) · 2 marks

Given the chance the first 3 occurs on spin n is 729/16384, determine n.

  1. 1P(not 3) = 3/4, P(3) = 1/4
  2. 2(3/4)ⁿ⁻¹ × 1/4 = 729/16384
  3. 3729 = 3⁶ and 16384 = 4⁷, so (3/4)⁶ × 1/4 = 3⁶/4⁷
  4. 4n − 1 = 6, so n = 7

Answer7

Part (bi) · 2 marks

Using 0.9 for theory and 0.8 for practical, find the chance Scott passes both and so passes the exam.

  1. 1P(pass both) = 0.9 × 0.8
  2. 2= 0.72

Answer0.72

Part (bii) · 3 marks

Find the probability Scott passes exactly one of the two tests, not both.

  1. 1P(pass theory, fail practical) = 0.9 × 0.2 = 0.18
  2. 2P(fail theory, pass practical) = 0.1 × 0.8 = 0.08
  3. 3P(exactly one) = 0.18 + 0.08 = 0.26

Answer0.26

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

Practise more tree diagrams for independent events questions

Real 0580 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 independent events

Also searched as: 0580/43/O/N/21 · 0580_w21_qp_43 · 0580 w21 43 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.