EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Experimental Probability
Experimental probability · Probability · Lesson 3 of 6 · 16 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 CALCULATOR (2 marks)
A spinner is spun 60 times. It lands on red 18 times. Work out the relative frequency of red.
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(Total for Question 1 = 2 marks)
Question 2 CALCULATOR (3 marks)
A spinner is spun 200 times. It lands on red 62 times. Work out an estimate for the number of times it will land on red in 500 spins.
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(Total for Question 2 = 3 marks)
Question 3 CALCULATOR (3 marks)
The graph shows the relative frequency of heads as a coin is tossed more and more times. Use it to explain whether the coin is likely to be fair.
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(Total for Question 3 = 3 marks)
Question 4 CALCULATOR (3 marks)
A dice is rolled 120 times. It lands on 6 a total of 30 times. Kim says the dice is biased. Is she right? You must show working.
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(Total for Question 4 = 3 marks)
Question 5 CALCULATOR (3 marks)
The probability that a bus is late is 0.15. Work out the expected number of late buses in 200 journeys.
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(Total for Question 5 = 3 marks)
Question 6 EXPLAIN (2 marks)
Amy tosses a coin 10 times and gets 7 heads. Ben tosses the same coin 1000 times and gets 505 heads. Whose result gives a better estimate of the probability of a head? Give a reason.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
18/60 = 0.3.
• 18/60 M1
• 0.3 A1
Question 2 (3 marks)
The relative frequency is 62/200 = 0.31. The expected number is 0.31 × 500 = 155.
• 62/200 M1
• 0.31 × 500 M1
• 155 A1
Question 3 (3 marks)
The relative frequency gets close to 0.5 as the number of tosses increases, so the coin is likely to be fair.
• The relative frequency settles M1
• It is near 0.5 M1
• Conclusion that the coin is likely to be fair C1
Question 4 (3 marks)
The relative frequency of a 6 is 30/120 = 0.25, compared with 1/6 ≈ 0.17 for a fair dice. The expected number of sixes is 20. 30 is much higher, so the dice may be biased, but more trials would make the conclusion more reliable.
• 30/120 = 0.25 or expected 20 M1
• Comparison with 1/6 or 20 M1
• A conclusion with a reason C1
Question 5 (3 marks)
0.15 × 200 = 30.
• 0.15 × 200 M1
• 30 A1
• A sensible unit or statement B1
Question 6 (2 marks)
Ben's result, because he did many more trials, so his relative frequency (0.505) is more reliable.
• Ben B1
• More trials give a more reliable estimate C1