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0580/43 May/Jun 2021, Question 6: Conditional Probability

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

Use the given counts for 24 students, 18 liking H, 15 liking T and 1 liking neither to complete a Venn diagram and answer related counting and probability questions.

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

Part (a) · 2 marks

Fill the three blank regions of the Venn diagram using the totals and the 1 outside both circles.

  1. 1In H or T: 24 − 1 = 23
  2. 2Both: 18 + 15 − 23 = 10
  3. 3H only: 18 − 10 = 8; T only: 15 − 10 = 5
  4. 4H only 8, H ∩ T 10, T only 5, outside 1

AnswerH only: 8 H ∩ T: 10 T only: 5 Outside H and T: 1

Part (b) · 1 mark

State how many students are in the overlap of homework and tests.

  1. 1From the Venn diagram, H ∩ T = 10

Answer10

Part (c) · 1 mark

Find the number of students in T only, that is outside H but inside T.

  1. 1H′ ∩ T is T only = 5

Answer5

Part (d) · 1 mark

Give the probability a randomly chosen student likes tests but not homework.

  1. 1T only = 5 out of 24 students
  2. 2P = 5/24

Answer5/24

Part (e) · 1 mark

Find the probability that two students chosen at random both like neither homework nor tests.

  1. 1Only 1 student likes neither
  2. 2P = 1/24 × 0/23 = 0

Answer0

Part (f) · 3 marks

Given two students who like homework are chosen, find the probability both also like tests.

  1. 110 of the 18 homework-likers also like tests
  2. 2P = 10/18 × 9/17 = 90/306
  3. 3= 5/17

Answer5/17

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Also searched as: 0580/43/M/J/21 · 0580_s21_qp_43 · 0580 s21 43 · question 6.
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