EDEXCEL GCSE MATHS · HIGHER
Exam Practice: Conditional Probability
Conditional probability · Probability · Lesson 5 of 6 · 18 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 NON-CALCULATOR (3 marks)
A bag contains 5 red counters and 3 blue counters. Two counters are taken at random without replacement. Work out the probability that both counters are red.
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(Total for Question 1 = 3 marks)
Question 2 NON-CALCULATOR (3 marks)
For the same bag, work out the probability that the two counters are different colours.
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(Total for Question 2 = 3 marks)
Question 3 NON-CALCULATOR (3 marks)
A bag contains 4 red counters and 6 blue counters. Two counters are taken at random without replacement. Complete the tree diagram.
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(Total for Question 3 = 3 marks)
Question 4 NON-CALCULATOR (3 marks)
Using the tree diagram, work out the probability that both counters are blue.
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(Total for Question 4 = 3 marks)
Question 5 NON-CALCULATOR (3 marks)
Using the tree diagram, work out the probability that at least one of the counters is red.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (3 marks)
60 students were asked whether they like football. 35 like football, and 20 of these are boys. 30 of the 60 students are boys. A student is chosen at random. Given that the student likes football, work out the probability that they are a boy.
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 18 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
⅝ × 4/7 = 20/56 = 5/14.
• ⅝ M1
• ⅝ × 4/7 M1
• 5/14 A1
Question 2 (3 marks)
⅝ × 3/7 + ⅜ × 5/7 = 15/56 + 15/56 = 15/28.
• One correct product M1
• Adding both orders M1
• 15/28 A1
Question 3 (3 marks)
After red: red 3/9 and blue 6/9. After blue: red 4/9 and blue 5/9.
• Denominator 9 on all four branches B1
• After red: 3/9, 6/9 B1
• After blue: 4/9, 5/9 B1
Question 4 (3 marks)
6/10 × 5/9 = 30/90 = ⅓.
• 6/10 × 5/9 M1
• 30/90 A1
• ⅓ A1
Question 5 (3 marks)
1 − P(both blue) = 1 − ⅓ = ⅔.
• 1 − P(both blue) M1
• 1 − ⅓ M1
• ⅔ A1
Question 6 (3 marks)
Of the 35 who like football, 20 are boys. The probability is 20/35 = 4/7.
• 35 as the total M1
• 20/35 A1
• 4/7 A1