Leaving Cert Maths: Probability
How often Probability comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
FL Asked on 7 of the last 7 Foundation Level papers, most recently in 2026. banker
Quick ones on Probability.
- 20
- 10
- 7
- 10
- 16
- 24
- 0.7
- 1.3
- 0.3
Show the answers
(a) 10
(b) 24
(c) 0.7
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q5, Q8, Q10 |
| 2025 | Q3, Q9, Q10 |
| 2024 | Q2, Q6, Q7, Q10 |
| 2023 | Q1, Q8, Q10 |
| 2022 | Q1, Q8, Q10 |
| 2021 | Q1, Q8, Q10 |
| 2019 | Q1, Q6 |
| 2018 | Q1, Q3 |
| 2017 | Q1, Q8, Q9 |
| 2016 | Q5, Q6 |
Links open the State Examinations Commission’s paper for that year.
More Probability questions
Probability, 2 marks
Expected value of a random variable, E(X) = ?
- Σ P(x)
- Σ x
- Σ x·P(x)
Show the answer
Σ x·P(x)
Multiply each value by its probability and add them all up. It's the long-run average value of X.
Probability, 2 marks
P(exactly r successes in n Bernoulli trials)?
- ⁿCᵣ pⁿqʳ
- ⁿCᵣ pʳqⁿ⁻ʳ
- pʳqⁿ⁻ʳ
Show the answer
ⁿCᵣ pʳqⁿ⁻ʳ
Choose which r trials are the successes (ⁿCᵣ ways); each such outcome has probability pʳqⁿ⁻ʳ, where q = 1 − p.
Probability, 2 marks
A fair die is rolled. P(score greater than 4)?
- 1/3
- 1/2
- 2/3
Show the answer
1/3
Scores greater than 4 are 5 and 6: 2 outcomes out of 6, so 2/6 = 1/3.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q2, Q3, Q5 |
| 2025 | Q7, Q10 |
| 2024 | Q2, Q5, Q9 |
| 2023 | Q3, Q4, Q10 |
| 2022 | Q3, Q7, Q10 |
| 2021 | Q1, Q2 |
| 2019 | Q1, Q3 |
| 2018 | Q1, Q3 |
| 2017 | Q1, Q5 |
| 2016 | Q1 |
Links open the State Examinations Commission’s paper for that year.
More Probability questions
Probability, 2 marks
A fair coin is tossed once. What is P(head)?
- 1
- 1/4
- 1/2
Show the answer
1/2
There are 2 equally likely outcomes and 1 of them is a head, so P = 1/2.
Probability, 2 marks
A fair die is rolled. What is P(5)?
- 1/5
- 1/6
- 5/6
Show the answer
1/6
One of the 6 equally likely faces is a 5, so P = 1/6.
Probability, 2 marks
P(A) = 0.4. What is P(not A)?
- 0.6
- 0.4
- 1.4
Show the answer
0.6
A and not A cover everything, so P(not A) = 1 − P(A) = 1 − 0.4 = 0.6.
Foundation Level
Asked on 7 of the last 7 Foundation Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q3, Q9 |
| 2025 | Q3 |
| 2024 | Q2, Q4, Q7 |
| 2023 | Q4, Q7, Q10 |
| 2022 | Q6, Q9 |
| 2021 | Q7, Q11 |
| 2019 | Q2 |
Links open the State Examinations Commission’s paper for that year.
More Probability questions
Probability, 2 marks
A fair coin is tossed. What is the probability of getting a head?
- 1
- 2
- 1/2
Show the answer
1/2
There are 2 equally likely outcomes, head or tail. One of them is a head, so the probability is 1/2.
Probability, 2 marks
A fair die is rolled. What is the probability of getting a 5?
- 1/5
- 1/6
- 5/6
Show the answer
1/6
A die has 6 equally likely numbers. Only one of them is a 5, so the probability is 1/6.
Probability, 2 marks
Which probability means that an event is certain?
- 1
- 0
- 0.5
Show the answer
1
Probabilities go from 0 (impossible) to 1 (certain). Certain is 1.