EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Mutually Exclusive Events
Mutually exclusive events · Probability · Lesson 2 of 6 · 15 marks · 25 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 biased spinner lands on red with probability 0.3, on blue with probability 0.5, and otherwise on green. Work out the probability that the spinner lands on green.
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(Total for Question 1 = 2 marks)
Question 2 NON-CALCULATOR (2 marks)
The probability that it rains tomorrow is 0.35. Work out the probability that it does not rain tomorrow.
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(Total for Question 2 = 2 marks)
Question 3 NON-CALCULATOR (3 marks)
A four-sided spinner is biased. The probability of each score is shown: score 1: 0.1, score 2: 0.25, score 3: x, score 4: 0.3. Work out the value of x, and the probability of scoring 2 or 4.
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(Total for Question 3 = 3 marks)
Question 4 NON-CALCULATOR (2 marks)
A bag has 5 red counters, 3 blue counters and 2 green counters. One counter is taken at random. Work out the probability that it is red or green.
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(Total for Question 4 = 2 marks)
Question 5 NON-CALCULATOR (3 marks)
In a class of 30 students, 12 play football, 9 play tennis and 5 play both. Explain why the events "plays football" and "plays tennis" are not mutually exclusive.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (3 marks)
A and B are two events. P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. Work out P(A or B).
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 15 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
1 − 0.3 − 0.5 = 0.2.
• 1 − 0.3 − 0.5 M1
• 0.2 A1
Question 2 (2 marks)
1 − 0.35 = 0.65.
• 1 − 0.35 M1
• 0.65 A1
Question 3 (3 marks)
0.1 + 0.25 + x + 0.3 = 1, so x = 0.35. P(2 or 4) = 0.25 + 0.3 = 0.55.
• Probabilities sum to 1 M1
• x = 0.35 A1
• 0.55 A1
Question 4 (2 marks)
5/10 + 2/10 = 7/10.
• Red and green probabilities added M1
• 7/10 A1
Question 5 (3 marks)
Five students play both, so the two events can happen at the same time, and they are not mutually exclusive.
• Reference to the 5 who play both M1
• Both events can happen together C1
• A clear conclusion C1
Question 6 (3 marks)
P(A or B) = 0.5 + 0.4 − 0.2 = 0.7.
• 0.5 + 0.4 M1
• Subtracting the overlap M1
• 0.7 A1