Edexcel IGCSE Maths
Topic questions Statistics Possibility spaces and combined events
23 questions · 92 marks · about 2 hours
Tamsin asked some people how they prefer their eggs cooked. They could choose scrambled or boiled or poached or fried.
The pie chart shows some information about their answers.
Use the pie chart to complete the table.
One of these people is selected at random.
Write down the probability that this person chose scrambled.
Remy chooses one food item and one drink for his breakfast.
He can choose one food item from cereal (C) or fruit (F) or a pastry (P) He can choose one drink from milk (M) or juice (J) or tea (T)
Write down all the possible combinations that Remy can choose.
Ahmed and Bryn share some blueberries in the ratio 3: 4
What fraction of the blueberries does Bryn get?
The children at a holiday club play sport either on Monday or on Tuesday. They each choose one sport from tennis or athletics or cricket. The two‑way table shows some information about their choices.
Complete the two‑way table.
One of the children who plays cricket is chosen at random.
Write down the probability that this child plays cricket on Monday.
Also involves The four operations
Joseph has some counters in a bag.
7 of the counters are red 5 of the counters are blue The rest of the counters are green
Joseph is going to take at random a counter from the bag. The probability that the counter is green is 
Work out the number of green counters in the bag.
Kate has a fair triangular spinner and a fair square spinner.
The triangular spinner can land on 2 or 4 or 6 The square spinner can land on 1 or 2 or 3 or 4
Kate spins each spinner once. She adds the number the triangular spinner lands on to the number the square spinner lands on to get her score.
Complete the table to show all possible scores. Four of the scores have been done for you.
Kate spins each spinner once.
Find the probability that her score is 9 or less.
A café sells 4 different types of cake.
carrot (C) fruit (F) lemon (L) madeira (M)
Nala is going to choose 2 different types of cake.
Write down all the possible combinations she can choose.
The two-way table gives some information about the flavours of ice creams sold by the café on Saturday and on Sunday.
Complete the two-way table.
Nala asks 100 students whether they prefer cake or ice cream.
33 of the students prefer cake.
One of the 100 students is chosen at random.
Find the probability that this student does not prefer cake.
The diagram shows a fair spinner with six sections.
Three sections are red, two sections are blue and one section is yellow.
The spinner is spun once.
Write down a word from the box to describe the likelihood that the spinner lands on yellow.
On the probability scale, mark with a cross (
) the probability that the spinner lands on green.
Here are 8 number cards. 3 of the number cards are blank.
Hugo is going to take at random one of these cards.
Write a number on each of the 3 blank cards so that the probability that Hugo picks a card with an odd number is 
Moeen has a biased 6-sided dice.
The table gives information about the probability that, when the dice is thrown, it will land on each number.
| Number | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | x | 0.15 | 0.5 | y | 0.13 | 0.03 |
Show that x + y = 0.19
Given that 3x – y = 0.09
and x + y = 0.19
work out the value of x and the value of y Show clear algebraic working.
Also involves The four operations
Avner has two fair spinners.
Spinner A
Spinner B
Spinner A can land on 1, 2 or 3 Spinner B can land on 1, 2, 3 or 4
Avner multiplies the number on which spinner A lands by the number on which spinner B lands to find his score.
Complete the table to show all possible scores. Seven of the scores have been completed for you.
Avner spins spinner A once and spinner B once.
Find the probability that his score is an odd number.
Linford is going to take part in an athletics competition. He can choose one event from List A and one event from List B
| List A | List B |
| Discus (D) Hammer (H) Javelin (J) Shot Put (S) | Long Jump (L) Pole Vault (P) Relay (R) |
Write down all the possible combinations Linford can choose.
Mario is going to play two games on Saturday. He will play one game on Saturday morning and one game on Saturday afternoon.
The following table shows the games from which he is going to choose.
| Morning | Afternoon |
| Bridge (B) Chess (C) Draughts (D) | Ludo (L) Mahjong (M) Snakes and ladders (S) |
Write down all the possible combinations of games that Mario can play on Saturday.
Mario asked 100 students in his school to name their favourite card game.
His results are shown in the two‑way table below.
| Solitaire | Rummy | Whist | Total | |
| Year 10 | 30 | 19 | 4 | 53 |
| Year 11 | 17 | 18 | 12 | 47 |
| Total | 47 | 37 | 16 | 100 |
One of the students Mario asked is picked at random.
Write down the probability that this student is in Year 11
One of the Year 10 students is picked at random.
Work out the probability that this student did not answer Whist.
Also involves The four operations
Bohai works in a shop that sells mobile phones. Last week he sold one mobile phone to each of 300 customers.
The incomplete two‑way table shows some information about these mobile phones.
Complete the two‑way table.
Bohai selects at random one of these 300 customers.
Write down the probability that this customer bought a type B, 64 GB mobile phone.
Bohai now selects at random one of the customers who bought a type A phone last week.
Write down the probability that this customer bought a 128 GB mobile phone.
At school each week, Gabriella has to play a sport on Monday and a sport on Thursday.
The table shows the sports from which she can choose on Monday and the sports from which she can choose on Thursday.
| Monday | Thursday |
| Tennis (T) | Volleyball (V) |
| Netball (N) | Badminton (B) |
| Hockey (H) | Tennis (T) |
Write down all the possible combinations of these sports that Gabriella can play in one week.
A tin contains tea bags with a choice of four different flavours of tea. The four flavours of tea are Assam or Darjeeling or Nilgiri or Rize.
Sara takes at random a tea bag from the tin.
The table shows each of the probabilities that the flavour of the tea Sara takes is Assam or Darjeeling or Rize.
| Flavour of tea | Assam | Darjeeling | Nilgiri | Rize |
| Probability | 0.38 | 0.24 | 0.16 |
Work out the probability that the flavour of the tea Sara takes is Nilgiri.
Work out the probability that the flavour of the tea Sara takes is either Darjeeling or Rize.
Also involves Forming and solving equations
There are 54 fish in a tank. Some of the fish are white and the rest of the fish are red.
Jeevan takes at random a fish from the tank. The probability that he takes a white fish is 
Work out the number of white fish originally in the tank.
Jeevan puts the fish he took out, back into the tank. He puts some more white fish into the tank.
Jeevan takes at random a fish from the tank. The probability that he takes a white fish is now 
Work out the number of white fish Jeevan put into the tank.
E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {2, 4, 6, 8, 10, 12} B = {3, 6, 9, 12}
Complete the Venn diagram below for the setsE, A and B.
One of the numbers inE is to be chosen at random.
Find the probability that this number is not in set A and not in set B.
Also involves The four operations
Grace has a fair spinner and a fair dice.
The spinner is 3-sided and can land on 6, 7 or 8 The dice can land on 1, 2, 3, 4, 5 or 6
Grace spins the spinner once and throws the dice once.
Grace subtracts the number that the dice lands on from the number that the spinner lands on to get her score.
Complete the table to show all possible scores. Eight of the scores have been done for you.
Grace spins the spinner once and throws the dice once.
Find the probability that her score is less than 6
Find the probability that her score is an odd number.
Here are two fair spinners.
Spinner A Spinner B
Chanthira spins each spinner once.
She adds together the number that spinner A lands on and the number that spinner B lands on to find the score.
Complete the table to show all possible scores. Three scores have been done for you.
Find the probability that the score will be 4 or less.
Chanthira now spins both spinners together 84 times.
Find an estimate for the number of times that spinner A and spinner B land on the same number.
Also involves Systematic listing and the product rule for counting
Paul is buying a sandwich and a drink in a meal deal.
He can have a cheese sandwich (C) or an egg sandwich (E) or a tomato sandwich (T). He can have orange juice (O) or milk (M) or water (W) to drink.
Write down all the possible combinations Paul can buy.
Write down all the possible combinations that Mohsen can choose.
Find the probability that Mohsen chooses the red shirt to wear to the party.
There are 20 counters in a bag.
4 of the counters are pink. 9 of the counters are white. The rest of the counters are black.
Jean takes at random one counter from the bag.
Work out the probability that Jean takes a black counter.
Also involves The four operations
Lin has 60 bricks. He puts his 60 bricks into a bag.
Some information about the 60 bricks is shown in the two-way table.
Complete the two-way table.
One of the bricks is taken at random from the bag.
Write down the probability that this brick is blue.
Lin now puts all his large bricks into a sack. He takes at random a large brick from the sack.
Write down the probability that this large brick is orange.
Also involves Mutually exclusive and independent events
There are some ice lollies in a freezer.
The flavour of each ice lolly is banana or strawberry or mint or chocolate.
Julius takes at random an ice lolly from the freezer.
The table shows the probabilities that the flavour of the ice lolly that Julius takes is banana or strawberry or chocolate.
| Flavour | banana | strawberry | mint | chocolate |
| Probability | 0.35 | 0.32 | 0.12 |
Work out the probability that the flavour of the ice lolly that Julius takes is either strawberry or mint.
Javier has two sets of cards. Each set contains 4 cards, one marked A, one marked B, one marked C and one marked D.
Javier is going to take at random one card from each set. The table shows all possible pairs of cards that Javier could take.
| A | B | C | D | |
| A | AA | AB | AC | AD |
| B | BA | BB | BC | BD |
| C | CA | CB | CC | CD |
| D | DA | DB | DC | DD |
Find the probability that Javier will take at least one card marked C.
Javier is going to take at random one card from each set, note the letter on each card and replace the cards.
He is going to do this a total of 80 times.
Work out an estimate for the number of times that Javier will take at least one card marked C.
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