Karnataka 2nd PUC Maths Chapter 13 Important Questions: Probability

Karnataka 2nd PUC Maths Chapter 13, Probability, covers concepts such as sample space, events, conditional probability, independent events, multiplication theorem, total probability theorem, and Bayes’ theorem. Regular practice of different types of probability problems helps students understand how these concepts are applied in different situations.

The Karnataka 2nd PUC Maths Chapter 13 Important Questions 2027 include objective questions based on the concepts covered in the chapter. The Karnataka Mathematics CET PDF contains questions on dice, coins, playing cards, selection of objects, conditional events, independent events, and applications of different probability theorems.

Students can use these questions for revision and practise the concepts before attempting mixed questions. The PDF also includes KCET Previous Year Questions from different years, which can be used for additional practice.

Probability Important Questions PDF

Students preparing for the Karnataka 2nd PUC examination can use the Probability Important Questions PDF for focused practice. The Karnataka Government Mathematics II PUC contains chapter-wise MCQs covering Probability and includes separate sections for Conditional Probability, Independent Events, Multiplication Theorem, Total Probability Theorem, and Bayes’ Theorem.

Karnataka 2nd PUC Probability Important Questions

The chapter begins with basic concepts such as sample space and events. The PDF gives sample spaces for tossing coins and throwing dice, along with basic information about playing cards. It then moves to conditional probability, independent events, the multiplication theorem, the total probability theorem, and Bayes’ theorem.

Important topics to revise include:

• Sample Space and Events

• Probability of an Event

• Conditional Probability

• Independent Events

• Multiplication Theorem of Probability

• Total Probability Theorem

• Bayes’ Theorem

• Selection of Objects With and Without Replacement

• Probability Based on Coins, Dice and Playing Cards

• KCET Previous Year Questions

These topics form the basis of the 2nd PUC Probability Important Questions given in the chapter-wise.

Probability 1 Mark Questions

The 1-mark questions generally focus on definitions, basic concepts, direct formula applications and simple probability situations. Students should revise the basic properties of probability before solving these questions.

Some questions from the PDF include:

Question 1: A coin is flipped and a dice is rolled. Which of the following statements is correct?

Statement 1: The probability of getting a tail and a 6 is 1/12.

Statement 2: The probability of getting a tail and not 6 is 5/12.

A) Statement 1 is true, and Statement 2 is false
B) Statement 1 is true, and Statement 2 is true
C) Statement 1 is false, and Statement 2 is true
D) Statement 1 is false, and Statement 2 is false

Question 2: Two cards are drawn at random without replacement from a pack of 52 playing cards. The probability that both are black cards is:

A) 1/26
B) 1/4
C) 25/102
D) 25/104

Question 3: Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. The probability that both are red is:

A) 25/81
B) 16/81
C) 20/81
D) 28/153

Probability 2 Mark Questions

For short-answer preparation, students should practise questions that require direct application of conditional probability and the multiplication theorem.

Question 1: A class has 7 boys and 5 girls. Three students are selected one after another without replacement. The probability that all three are girls is:

A) 5/66
B) 1/22
C) 5/44
D) 1/11

Question 2: A factory has 6 good and 4 defective products. Two products are selected without replacement. If the first product is good, what is the probability that both selected products are good?

A) 1/3
B) 2/5
C) 1/2
D) 1/5

Question 3: A flashlight has 8 batteries, out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is:

A) 33/56
B) 9/64
C) 1/14
D) 3/28

Probability 3/5 Mark Questions

The longer questions in Probability require students to apply more than one concept or solve a problem through multiple steps. Questions involving the multiplication theorem, total probability, and Bayes’ theorem are useful for this type of practice.

Question 1: The probability of solving a specific problem independently by A and B are 1/2 and 1/3, respectively. If both try to solve the problem, the probability that the problem is solved is:

A) 1/6
B) 2/3
C) 1/3
D) 5/6

Question 2: Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. The probability that one of them is black and the other is red is:

A) 40/81
B) 20/81
C) 16/81
D) 56/153

Question 3: Three buses A, B and C carry 20%, 35% and 45% of the students to a college. The probabilities that a student reaches late are 0.15, 0.8 and 0.2 respectively. Find the probability that a randomly selected student reaches on time.

A) 0.4
B) 0.8
C) 0.6
D) 0.2

Conditional Probability Important Questions

Conditional probability deals with finding the probability of an event when information about another event is already known. The PDF contains a separate set of 50 MCQs on Conditional Probability.

Important Conditional Probability Questions include:

Question 1: In a college, 30% of students fail in Physics, 25% fail in Mathematics, and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics, is:

A) 1/10
B) 2/5
C) 9/20
D) 1/3

Question 2: Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, the probability of getting a sum of 3 is:

A) 1/18
B) 5/18
C) 1/5
D) 2/5

Question 3: If P(A|B) = 0.8 and P(B|A) = 0.5, then the ratio P(A)(B) is:

A) 8:5
B) 5:8
C) 2:5
D) 1:2

Students should pay particular attention to the difference between P(A|B) and P(B|A) while solving these questions.

Bayes Theorem Important Questions

Bayes’ theorem is used in questions where an event has occurred, and the probability of a particular cause needs to be determined. The PDF includes questions based on students, examination centres, manufacturing defects, medical tests, and other real-life situations.

Some important Bayes Theorem Questions are given below.

Question 1: The probability that A speaks truth is 4/5. A coin is tossed. A reports that a head appears. The probability that actually there was a head is:

A) 4/5
B) 1/2
C) 1/5
D) 2/5

Question 2: An investigation finds that 5% of examination centres had a paper leak before the exam. A monitoring system raises an alert for 90% of centres where a leak occurred and also raises a false alert for 10% of centres where there was no leak. If a centre is found to have an alert, what is the probability that a paper leak actually occurred?

A) 9/28
B) 9/47
C) 18/47
D) 9/19

Question 3: In a factory, machines A, B and C manufacture 25%, 35% and 40% of the bolts respectively. Of their outputs, 5%, 4% and 2% are defective, respectively. A bolt is drawn at random and is found to be defective. What is the probability that it was manufactured by machine B?

A) 8/69
B) 28/69
C) 18/69
D) 38/69

Probability MCQs and Previous Year Questions

The chapter contains a dedicated KCET PYQs section. It includes questions from KCET 2026, 2025, 2023, 2022, 2021 and earlier years. Some of the Probability Previous Year Questions include:

• A KCET 2026 question based on the probability of a child being left-handed depending on whether the parents are left-handed or right-handed.

• A KCET 2026 question involving the probability that a man and his wife live after 20 years.

• A KCET 2025 question involving the relationship between P(A|B) and P(B|A).

• A KCET 2025 Bayes’ theorem question involving Meera visiting one of two temples and meeting her friend.

• A KCET 2023 question involving a bag containing coins with different properties.

• A KCET 2023 question involving the probability that a randomly selected function is onto.

The PDF also provides answer keys for the different MCQ sections, including Conditional Probability, Independent Events, Multiplication Theorem, Total Probability Theorem and Bayes’ Theorem.

Important Topics for Karnataka 2nd PUC Maths Chapter 13

Students should revise the following topics before attempting the complete question set:

• Sample Space

• Events

• Probability of an Event

• Conditional Probability

• Independent Events

• Multiplication Theorem of Probability

• Total Probability Theorem

• Bayes’ Theorem

• Problems Based on Cards, Coins and Dice

• Problems With and Without Replacement

• KCET Previous Year Questions

The PDF begins with sample spaces for coins and dice and then progresses towards conditional probability and the major probability theorems.

How to Prepare Karnataka 2nd PUC Maths Chapter 13 Important Questions 2027?

Students can follow these steps while preparing Probability:

1. Revise the basic concepts first: Understand sample space, events, complements, union, and intersection before moving to conditional probability.

2. Practise one concept at a time: Complete the Conditional Probability questions first, followed by Independent Events and the Multiplication Theorem.

3. Focus on application-based questions: Practise questions involving cards, dice, coins, balls, and selection without replacement.

4. Practise Total Probability and Bayes’ Theorem separately: Identify the given events and the required probability before selecting the appropriate theorem.

5. Solve the MCQs without checking the answer key: Mark your answers first and then compare them with the answer key provided in the PDF.

6. Attempt KCET previous-year questions: Solve the PYQs after completing the concept-wise questions to practise mixed applications of Probability.

Probability becomes easier with regular practice of different types of events and numerical situations. Students should revise the basic concepts first and then practise conditional probability, independent events, multiplication theorem, total probability theorem and Bayes’ theorem.

The chapter-wise material provides MCQs, concept-based questions, Exemplar questions and KCET previous-year questions for practice. Using these questions along with the prescribed syllabus can help students strengthen their preparation for the Karnataka 2nd PUC Maths Exam 2027.

Related Resources

• Karnataka 2nd PUC Mid Term Time Table 2026 

• Karnataka 2nd PUC Mid Term Question Paper

• Karnataka 2nd PUC Previous Year Question Paper 

• Karnataka 2nd PUC Exam Pattern 2027

• Karnataka 2nd PUC Syllabus 2026-27