Class 11 Maths Chapter 14 Probability – Exercise 14.1 NCERT Solutions

Introduction

Exercise 14.1 introduces the basic concepts of probability. You will learn definitions of random experiments, sample space, events, and how to calculate probability using classical and axiomatic approaches. This exercise builds the foundation for advanced probability in Class 11 and Class 12.

Key Concepts

1. Random Experiment: An experiment whose outcome cannot be predicted with certainty.

2. Sample Space (S): Set of all possible outcomes. Example: Toss of coin → $S=\{H,T\}$.

3. Event (E): Subset of sample space. Example: Getting head in coin toss → $E=\{H\}$.

4. Probability of Event:

$$P(E)=\frac{n(E)}{n(S)}$$

where $n(E)$ = number of favorable outcomes, $n(S)$ = total outcomes.

NCERT Questions with Solutions (10)

Q1. A coin is tossed once. Find probability of getting head.

$$P(E)=\frac{1}{2}$$

Q2. A die is thrown once. Find probability of getting even number. Sample space = $\{1,2,3,4,5,6\}$. Favorable = $\{2,4,6\}$.

$$P(E)=\frac{3}{6}=\frac{1}{2}$$

Q3. A die is thrown once. Find probability of getting prime number. Prime outcomes = $\{2,3,5\}$.

$$P(E)=\frac{3}{6}=\frac{1}{2}$$

Q4. A coin is tossed twice. Find probability of getting two heads. Sample space = $\{HH,HT,TH,TT\}$. Favorable = $\{HH\}$.

$$P(E)=\frac{1}{4}$$

Q5. A coin is tossed twice. Find probability of getting at least one head. Favorable = $\{HH,HT,TH\}$.

$$P(E)=\frac{3}{4}$$

Q6. A die is thrown once. Find probability of getting number greater than 4. Favorable = $\{5,6\}$.

$$P(E)=\frac{2}{6}=\frac{1}{3}$$

Q7. A card is drawn from a deck of 52 cards. Find probability of getting ace. Favorable = 4 aces.

$$P(E)=\frac{4}{52}=\frac{1}{13}$$

Q8. A card is drawn from a deck of 52 cards. Find probability of getting red card. Favorable = 26 red cards.

$$P(E)=\frac{26}{52}=\frac{1}{2}$$

Q9. A card is drawn from a deck of 52 cards. Find probability of getting king. Favorable = 4 kings.

$$P(E)=\frac{4}{52}=\frac{1}{13}$$

Q10. A card is drawn from a deck of 52 cards. Find probability of getting face card. Face cards = J, Q, K → 12 cards.

$$P(E)=\frac{12}{52}=\frac{3}{13}$$

FAQs (10)

1. What is probability? Measure of chance of occurrence of event.

2. What is sample space? Set of all possible outcomes.

3. What is event? Subset of sample space.

4. What is probability formula? $\frac{n(E)}{n(S)}$.

5. Can probability be negative? No, always between 0 and 1.

6. What is probability of sure event? Equal to 1.

7. What is probability of impossible event? Equal to 0.

8. What is classical approach of probability? Ratio of favorable outcomes to total outcomes.

9. What is axiomatic approach? Probability defined using axioms.

10. Why is this exercise important? It builds foundation for advanced probability and statistics.

Conclusion

Exercise 14.1 has 10 solved questions and 10 FAQs that strengthen your understanding of basic probability concepts. This builds the foundation for advanced probability in Class 11 Maths.

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New CBSE Syllabus,Class 11 Maths Chapter 14 Probability – Exercise 14.1 NCERT