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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Counting & probability

How often Counting & probability comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

OL Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Counting & probability, Higher Level(8 marks)

Quick ones on Counting & probability.

(a)A menu has 4 starters, 5 mains and 3 desserts. How many different 3-course meals are possible?
  1. 12
  2. 60
  3. 20
(b)Two fair dice are thrown. What is the probability that the total is 7?
  1. 7/36
  2. 1/12
  3. 1/6
(c)A fair coin is tossed 3 times. What is the probability of exactly 2 heads?
  1. 3/8
  2. 2/3
  3. 1/4
Show the answers

(a) 60

(b) 1/6

(c) 3/8

Your turn: Higher Level questions on Counting & probability.

Higher Level

Asked on 5 of the last 5 Higher Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q1
2025Q1, Q2
2024Q1
2023Q5
2022Q2

Links open the State Examinations Commission’s paper for that year.

Ordinary Level

Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q2, Q10
2025Q5, Q6, Q13
2024Q3
2023Q6
2022Q2, Q5

Links open the State Examinations Commission’s paper for that year.

More Counting & probability questions

Counting & probability, 2 marks

A fair die is rolled. What is P(a number greater than 4)?

  1. 1/2
  2. 2/3
  3. 1/3
Show the answer

1/3

Only 5 and 6 are greater than 4: 2 outcomes out of 6. P = 2/6 = 1/3.

Counting & probability, 2 marks

A café has 3 starters and 4 main courses. How many different meals of one starter and one main are there?

  1. 24
  2. 12
  3. 7
Show the answer

12

Fundamental principle of counting: multiply the choices. 3 starters × 4 mains = 12 different meals. Adding (7) is wrong.

Counting & probability, 2 marks

The probability that it rains tomorrow is 0.3. What is the probability that it does not rain?

  1. 0.7
  2. 0.3
  3. 1.3
Show the answer

0.7

It either rains or it doesn't, so the two probabilities add to 1: P(no rain) = 1 − 0.3 = 0.7.

Other Maths topics

All of Junior Cycle Maths