Edexcel GCSE Maths (1MA1), Higher tier · Probability
Practise Probability and relative frequency. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy3 marks
Kai spins a spinner 10 times. It lands on red 4 times.
(a) Kai says, 'The probability that the spinner lands on red is exactly 0.4.' Explain why Kai may be wrong.[1]
(b) Kai's friend spins the same spinner 200 times. It lands on red 60 times. Which gives the more reliable estimate of the probability of red, Kai's results or his friend's results? Give a reason.[1]
(c) Use the more reliable estimate to predict how many times the spinner would land on red in 500 spins.[1]
Show the answer and mark scheme
(a)Answer: 0.4 is only an estimate from a small number of spins (10); the true probability could be different.
C1 for explaining that the relative frequency is only an estimate, and 10 spins is a small number of trials
Worked solution: Results vary. 4 reds in 10 spins gives an estimate of the probability, not its exact value.
(b)Answer: His friend's (0.3), because it is based on many more spins.
C1 for the friend's results with the reason that there were more trials (200 compared with 10)
Worked solution: The more trials, the more reliable the relative frequency. 200 spins is far more than 10.
(c)Answer: 150
B1 for 150
Worked solution: \(\frac{60}{200} = 0.3\) and \(0.3 \times 500 = 150\).
Question 2Medium3 marks
At a school fair it costs 50p to play a game. A fair six-sided dice is rolled once. If the dice lands on 6, the player is given £2. Otherwise the player is given nothing. The 50p is never returned. The game is played 300 times.
Work out how much profit the school should expect to make from the game.[3]
Show the answer and mark scheme
Answer: £50
M1 for \(300 \times \frac{1}{6}\) (= 50 expected wins)
M1 for income \(300 \times 0.50\) (= £150) and prizes \(50 \times 2\) (= £100)
A1 for £50
Worked solution: Expected number of 6s \(= 300 \times \frac{1}{6} = 50\), so the prizes cost \(50 \times 2 = 100\) pounds. Money taken \(= 300 \times 0.50 = 150\) pounds. Expected profit \(= 150 - 100 = 50\) pounds.
Question 3Hard3 marks
A fair 10-sided dice, numbered 1 to 10, is rolled. Fatima says, “The probability of getting a factor of 12 or an even number is \(\frac{1}{2} + \frac{1}{2} = 1\).”
(a) Explain why Fatima is wrong.[1]
(b) Work out the correct probability of getting a factor of 12 or an even number.[2]
Show the answer and mark scheme
(a)Answer: The events are not mutually exclusive: 2, 4 and 6 are each a factor of 12 and an even number, so they have been counted twice.
C1 for a correct explanation, e.g. the events are not mutually exclusive because 2 is a factor of 12 and an even number, so it has been counted twice
Worked solution: Adding probabilities only works for mutually exclusive events. 2, 4 and 6 are each a factor of 12 and an even number, so Fatima has counted them twice.
(b)Answer: \(\frac{7}{10}\)
M1 for listing the 7 outcomes (1, 2, 3, 4, 6, 8, 10) or \(\frac{1}{2} + \frac{1}{2} - \frac{3}{10}\)
A1 for \(\frac{7}{10}\) oe
Worked solution: The outcomes that are a factor of 12 or an even number (or both) are 1, 2, 3, 4, 6, 8, 10: 7 out of 10. Probability \(= \frac{7}{10}\).