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CAT Probability questions with solutions

Basic and conditional probability. 20 questions from our 2016–2025 CAT pattern papers. Each has the answer and a full solution.

Also practise: Probability for JEE Main · Probability for JEE Advanced · Probability for NDA

CAT 2025

Find the probability that the sum of the numbers shown is a prime number.CAT 2025 Slot 2 · medium
A bag contains 5 red balls and 7 blue balls. Three balls are drawn at random without replacement. The probability that all three balls drawn are of…CAT 2025 Slot 3 · medium

CAT 2024

CAT 2023

A bag contains 5 red and 7 blue balls. The probability that both balls are of the same colour is p/q in lowest terms. Find p + q.CAT 2023 Slot 2 · medium
What is the probability that the product of the numbers obtained is divisible by 3?CAT 2023 Slot 3 · medium

CAT 2022

A bag contains 4 red, 5 blue and 6 green balls. What is the probability that both balls are of the same colour?CAT 2022 Slot 2 · easy

CAT 2021

Two fair six-sided dice are thrown. What is the probability that the product of the two numbers is a perfect square?CAT 2021 Slot 2 · easy
A bag contains 5 red, 4 blue and 3 green balls. What is the probability that both balls drawn are of the same colour?CAT 2021 Slot 3 · easy

CAT 2020

Two fair six-sided dice are rolled. Given that at least one die shows a 3, what is the probability that the sum of the two numbers is a prime number?CAT 2020 Slot 1 · hard
A pair of fair six-sided dice is rolled once. What is the probability that the sum of the two numbers obtained is a perfect square?CAT 2020 Slot 2 · medium
Two fair six-sided dice are thrown.CAT 2020 Slot 3 · medium

CAT 2019

CAT 2018

Two distinct numbers are selected at random from the integers 1 to 20. What is the probability that their product is divisible by 3?CAT 2018 Slot 1 · hard
Two fair dice are rolled.CAT 2018 Slot 2 · medium

CAT 2017

Two fair six-sided dice are thrown together.CAT 2017 Slot 1 · medium
Two fair six-sided dice are rolled together.CAT 2017 Slot 2 · medium

CAT 2016

Two fair dice are thrown together. What is the probability that the sum of the numbers shown is a prime number?CAT 2016 Slot 1 · easy
Two fair dice are thrown.CAT 2016 Slot 2 · medium