EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Independent Events and Tree Diagrams
Independent events and tree diagrams · Probability · Lesson 4 of 6 · 17 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 (2 marks)
A and B are independent events. P(A) = 0.3 and P(B) = 0.5. Work out P(A and B).
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(Total for Question 1 = 2 marks)
Question 2 NON-CALCULATOR (3 marks)
The probability that Amy is late for school on any day is 0.2. The tree diagram shows the probabilities for two days. Complete the tree diagram.
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(Total for Question 2 = 3 marks)
Question 3 NON-CALCULATOR (2 marks)
Using the tree diagram, work out the probability that Amy is late on both days.
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(Total for Question 3 = 2 marks)
Question 4 NON-CALCULATOR (3 marks)
Using the tree diagram, work out the probability that Amy is late on exactly one of the two days.
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(Total for Question 4 = 3 marks)
Question 5 NON-CALCULATOR (3 marks)
Work out the probability that Amy is late on at least one of the two days.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (4 marks)
A bag contains 3 red counters and 2 blue counters. A counter is taken at random, its colour is noted and it is replaced. A second counter is taken. Work out the probability that the two counters are the same colour.
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(Total for Question 6 = 4 marks)
TOTAL FOR PAPER = 17 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
0.3 × 0.5 = 0.15.
• 0.3 × 0.5 M1
• 0.15 A1
Question 2 (3 marks)
All four second-stage branches: Late 0.2 and Not late 0.8, after either first-day outcome.
• Late branches 0.2 on day 2 B1
• Not late branches 0.8 on day 2 B1
• All four correct B1
Question 3 (2 marks)
0.2 × 0.2 = 0.04.
• 0.2 × 0.2 M1
• 0.04 A1
Question 4 (3 marks)
0.2 × 0.8 + 0.8 × 0.2 = 0.16 + 0.16 = 0.32.
• One correct product M1
• Adding the two paths M1
• 0.32 A1
Question 5 (3 marks)
The probability of never being late is 0.8 × 0.8 = 0.64. So P(at least one) = 1 − 0.64 = 0.36.
• 0.8 × 0.8 M1
• 1 − 0.64 M1
• 0.36 A1
Question 6 (4 marks)
P(RR) = 3/5 × 3/5 = 9/25 and P(BB) = 2/5 × 2/5 = 4/25. Together: 13/25.
• 3/5 × 3/5 M1
• 2/5 × 2/5 M1
• Adding the two M1
• 13/25 A1