Free Combined events & tree diagrams questions for IGCSE Mathematics (0580), part of Probability. Each question has the answer and the marking points an examiner would look for.
Generate a full Combined Events & Tree Diagrams worksheet →All Probability questionsThe probability that it rains on any day is 0.4. The weather on different days is independent.
Find the probability that it rains on exactly one of two days.
Find the probability that it rains on at least one of three days.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.48 2 × 0.4 × 0.6 M1 0.48 A1 | 2 |
| (b) | 0.784 1 − 0.63 M1 0.784 A1 | 2 |
A bag contains 5 red counters and 3 blue counters. Two counters are taken at random from the bag, without replacement.
Find the probability that the two counters are different colours.
Find the probability that at least one of the counters is red.
Given that the two counters are the same colour, find the probability that they are both red.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 1528 58 × 37 M1 × 2 or add the two orders M1 1528 A1 | 3 |
| (b) | 2528 1 − 38 × 27 M1 2528 A1 | 2 |
| (c) | 1013 2056 ÷ 2656 M1 1013 A1 | 2 |
A box contains 5 red sweets and 3 green sweets. Sam takes a sweet at random, eats it, then takes another.
Draw a tree diagram and find the probability that both sweets are red.
Find the probability that the sweets are different colours.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 514 tree with correct branches B1 58 × 47 M1 514 A1 | 3 |
| (b) | 1528 2 × 58 × 37 M1 1528 A1 | 2 |
A bag contains 3 red counters and 2 blue counters.
Amira takes a counter at random, notes its colour and does not replace it. She then takes a second counter at random.
Complete the tree diagram.
Find the probability that both counters are red.
Find the probability that the counters are different colours.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | Lower branches: 3/4 and 1/4 3/4 B1 1/4 B1 | 2 |
| (b) | 310 35 × 24 M1 310 A1 | 2 |
| (c) | 35 35 × 24 M1 25 × 34 added M1 35 A1 | 3 |
A bag contains 6 red counters and n blue counters. Two counters are taken at random, without replacement.
The probability that the two counters are the same colour is 715.
Form an equation in n.
Solve the equation to find n.
The bag is returned to its original contents. Three counters are now taken without replacement. Find the probability that exactly two of them are red.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 15(30 + n2 − n) = 7(n + 6)(n + 5) or equivalent 6n + 6 × 5n + 5 + nn + 6 × n − 1n + 5 M1 combined over the common denominator M1 equated and cross-multiplied correctly A1 | 3 |
| (b) | n = 4 expanded to a quadratic = 0 M1 factorise / formula M1 n = 4 (reject the other root) A1 | 3 |
| (c) | 12 610 × 59 × 48 M1 × 3 for the arrangements M1 12 A1 | 3 |
Amir and Bea take turns to roll a fair six-sided die. Amir rolls first. The first person to roll a 6 wins.
Find the probability that Bea wins on her first roll.
Find the probability that Amir wins the game.
The rules change so that Bea wins if she rolls a 5 or a 6, while Amir still needs a 6. Determine whether the game is now fair.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 536 56 × 16 M1 536 A1 | 2 |
| (b) | p = 611 Amir wins at once with probability 16 B1 both miss with probability 2536, after which the game restarts M1 p = 16 + 2536p A1 1136p = 16 M1 p = 611 A1 | 5 |
| (c) | P(Amir) = 3/8, P(Bea) = 5/8: not fair, Bea favoured p = 16 + 56 × 23p M1 p = 38 A1 Bea wins with probability 58 A1 not fair A1 | 4 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in