Probability: Fluency and Exam Drill - Worksheets, Questions and Revision

19 original exam-style questions - 10 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics and Probability

2.12D Probability: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Match each event below to one word from the list: impossible, unlikely, evens, likely, certain.
(a)Rolling a 7 on a fair six-sided dice, numbered 1 to 6.(1)
(b)Picking a red card at random from a standard, well-shuffled pack of 52 playing cards.(1)
(c)The sun rising over Manchester tomorrow morning.(1)
(Total for Question 1 is 3 marks)
2
A bag contains 20 counters: 8 are lilac, 6 are grey and 6 are white. A counter is taken from the bag at random.
(a)Write down the probability that the counter is lilac.(1)
(b)Write down the probability that the counter is not grey.(1)
(c)Write down the probability that the counter is grey or white.(1)
(Total for Question 2 is 3 marks)
3
A café meal deal lets a customer choose one sandwich from cheese, tuna or ham, and one drink from tea, juice, water or hot chocolate.
(a)List all the possible sandwich-and-drink combinations a customer could choose.(2)
(b)A customer chooses a sandwich and a drink at random. Find the probability that they choose tuna and hot chocolate.(1)
(Total for Question 3 is 3 marks)
4
A fair spinner has 8 equal sections, numbered 1 to 8. The spinner is spun once.
(a)Find the probability that the spinner lands on a prime number.(1)
(b)Find the probability that the spinner lands on a multiple of 3.(1)
(c)Find the probability that the spinner lands on a factor of 8.(1)
(Total for Question 4 is 3 marks)
5
The two-way table shows information about 45 Year 11 students and whether they play a musical instrument.

Play instrument Do not play Total
Boys 9 ? 25
Girls ? 13 ?
Total ? ? 45

Some values in the table are missing (shown as ?).
(a)Complete the two-way table.(3)
(b)One student is picked at random from the 45. Find the probability that the student is a girl who plays an instrument.(1)
(Total for Question 5 is 4 marks)
6
The probability that the 42 bus from Leeds to Bradford arrives early is 0.15. The probability that it arrives on time is 0.62. The bus can only arrive early, on time or late.
(a)Work out the probability that the bus arrives late.(1)
(b)Work out the probability that the bus does not arrive early.(1)
(Total for Question 6 is 2 marks)
7
A bag contains only red, blue and green counters. P(red) = 0.25. The probability that a counter is blue is twice the probability that a counter is green.
(a)Find P(green).(2)
(b)Find P(blue).(1)
(c)There are 60 counters in the bag. Work out how many more blue counters than green counters there are.(2)
(Total for Question 7 is 5 marks)
8
Spinner A has three equal sections numbered 1, 2, 3. Spinner B has four equal sections numbered 1, 2, 3, 4. Both spinners are spun once and the two scores are added together to give a total score.
(a)Complete a sample space diagram to show all 12 possible total scores.(2)
(b)Find the probability that the total score is 5.(1)
(c)Find the probability that the total score is greater than 6.(1)
(Total for Question 8 is 4 marks)
9
A biased six-sided dice was rolled 150 times. The table shows the results.

Score 1 2 3 4 5 6
Frequency 18 22 19 20 26 45
(a)Find the relative frequency of rolling a 6.(1)
(b)Kofi rolls the same dice 400 times. Use the relative frequency from part (a) to estimate how many times it will land on a 6.(2)
(c)Comment on whether the dice appears to be fair. Give a reason for your answer.(1)
(Total for Question 9 is 4 marks)
10
A factory tests a random sample of 80 light bulbs from a production batch of 5000 bulbs. 6 of the sampled bulbs are found to be defective.
(a)Estimate the probability that a bulb from this batch is defective.(1)
(b)Use your answer to part (a) to estimate the number of defective bulbs in the whole batch of 5000.(2)
(c)The factory manager says: 'Since our sample found 6 defective bulbs out of 80, we can be certain that exactly 375 bulbs in the batch are defective.' Comment on whether the manager is correct.(1)
(Total for Question 10 is 4 marks)
11
In a class of 30 students, 18 are members of the Badminton Club, 15 are members of the Netball Club, and 7 are members of neither club.
(a)Find the number of students who are members of both clubs.(2)
(b)One student is selected at random from the class. Find the probability that the student is a member of the Badminton Club but not the Netball Club.(1)
(c)Given that a randomly selected student is a member of at least one of the two clubs, find the probability that they are a member of both.(2)
(Total for Question 11 is 5 marks)
12
Amara has a large bag of sweets. Each time she takes a sweet at random, notes its colour, and replaces it before taking the next one. The probability that a sweet taken at random is red is 0.4.
(a)Work out the probability that she picks a red sweet on both of her first two picks.(2)
(b)Work out the probability that she picks exactly one red sweet in her first two picks.(3)
(Total for Question 12 is 5 marks)
13
A biased spinner has two colours, orange and grey. The probability that it lands on orange is 0.55. The spinner is spun twice.
(a)Complete a probability tree diagram to show the possible outcomes of the two spins, with each branch labelled with a probability.(2)
(b)Work out the probability of getting exactly one orange.(3)
(c)Work out the probability of getting at least one orange.(2)
(Total for Question 13 is 7 marks)
14
A survey was carried out at Brightlow's supermarket of 200 customers. 65% of the customers shop online. Of the customers who shop online, 40% also use the loyalty app. Of the customers who do not shop online, 20% use the loyalty app.
(a)Work out the number of customers in the survey who shop online.(1)
(b)Work out the number of customers who shop online and use the loyalty app.(2)
(c)Find the probability that a customer selected at random from the survey does not use the loyalty app.(3)
(Total for Question 14 is 6 marks)
15
A bag contains 10 counters: 6 are teal and 4 are cream. Xin takes two counters from the bag at random, one after the other, without replacement.
(a)Work out the probability that both counters are teal.(2)
(b)Work out the probability that the two counters are different colours.(3)
(c)Given that the first counter taken is cream, find the probability that the second counter is also cream.(1)
(Total for Question 15 is 6 marks)
16
The two-way table shows information about 100 adults and whether they own a car.

Owns a car Does not own a car Total
Male 38 12 50
Female 29 21 50
Total 67 33 100
(a)Find the probability that a randomly selected adult owns a car.(1)
(b)Find the probability that the adult is female, given that they own a car.(2)
(c)Find the probability that the adult does not own a car, given that they are male.(2)
(Total for Question 16 is 5 marks)
17
The probability that Ben wins a game of chess against Farah is 0.65. Assume the results of the games are independent. They play three games.
(a)Work out the probability that Ben wins all three games.(2)
(b)Work out the probability that Ben wins at least one game.(2)
(Total for Question 17 is 4 marks)
18
In a class of 50 students, x study Biology only, 2x study Chemistry only, 8 study both Biology and Chemistry, and 9 study neither subject. Let B be the event that a student studies Biology and C be the event that a student studies Chemistry.
(a)Show that 3x + 17 = 50, and hence find the value of x.(3)
(b)Find P(B), the probability that a randomly selected student studies Biology.(2)
(c)Two students are then chosen at random, without replacement, from the whole class of 50 students. Find the probability that both students study neither subject.(2)
(Total for Question 18 is 7 marks)
19
A researcher claims that, for adults in a town, recycling regularly and owning a bicycle are independent events. In a sample of 400 adults, 220 recycle regularly, 180 own a bicycle, and 150 both recycle regularly and own a bicycle.
(a)Work out P(recycles regularly) x P(owns a bicycle), using the frequencies from the sample.(2)
(b)Work out P(recycles regularly and owns a bicycle), using the frequencies from the sample.(1)
(c)By comparing your answers to parts (a) and (b), determine whether the sample supports the researcher's claim that the two events are independent. Give a reason.(2)
(Total for Question 19 is 5 marks)
Mark scheme · 2.12D Probability: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19