Class 11 Maths Chapter 14 Probability – Exercise 14.2 NCERT Solutions

Introduction

Exercise 14.2 focuses on the addition theorem of probability. You will learn how to calculate probabilities of union of events, apply formulas for mutually exclusive and independent events, and solve problems involving combined probabilities. This exercise builds the foundation for advanced probability concepts in Class 12.

Key Concepts

1. Union of Two Events: For events $A$ and $B$:

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

2. Mutually Exclusive Events: If $A$ and $B$ cannot occur together, then

$$P(A\cup B)=P(A)+P(B)$$

3. Complementary Events:

$$P(A)+P(A^{\mathrm{\prime }})=1$$

4. Independent Events: If occurrence of one does not affect the other:

$$P(A\cap B)=P(A)\cdot P(B)$$

NCERT Questions with Solutions (10)

Q1. A card is drawn from a deck. Find probability of getting king or queen.

$$P(K\cup Q)=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}=\frac{2}{13}$$

Q2. A die is thrown once. Find probability of getting even number or prime number. Even = $\{2,4,6\}$, Prime = $\{2,3,5\}$. Union = $\{2,3,4,5,6\}$.

$$P(E)=\frac{5}{6}$$

Q3. A coin is tossed once. Find probability of getting head or tail.

$$P(H\cup T)=1$$

Q4. A card is drawn from deck. Find probability of getting ace or red card. Ace = 4, Red cards = 26, overlap = 2 red aces.

$$P(E)=\frac{4}{52}+\frac{26}{52}-\frac{2}{52}=\frac{28}{52}=\frac{7}{13}$$

Q5. A die is thrown once. Find probability of getting number >4 or even.

4 = $\{5,6\}$, Even = $\{2,4,6\}$. Union = $\{2,4,5,6\}$.

$$P(E)=\frac{4}{6}=\frac{2}{3}$$

Q6. A card is drawn. Find probability of getting spade or ace. Spades = 13, Aces = 4, overlap = 1 ace of spades.

$$P(E)=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$$

Q7. A die is thrown once. Find probability of getting odd number or prime number. Odd = $\{1,3,5\}$, Prime = $\{2,3,5\}$. Union = $\{1,2,3,5\}$.

$$P(E)=\frac{4}{6}=\frac{2}{3}$$

Q8. A card is drawn. Find probability of getting face card or red card. Face cards = 12, Red cards = 26, overlap = 6 red face cards.

$$P(E)=\frac{12}{52}+\frac{26}{52}-\frac{6}{52}=\frac{32}{52}=\frac{8}{13}$$

Q9. A die is thrown once. Find probability of getting multiple of 2 or 3. Multiples of 2 = $\{2,4,6\}$, multiples of 3 = $\{3,6\}$. Union = $\{2,3,4,6\}$.

$$P(E)=\frac{4}{6}=\frac{2}{3}$$

Q10. A card is drawn. Find probability of getting black card or king. Black cards = 26, Kings = 4, overlap = 2 black kings.

$$P(E)=\frac{26}{52}+\frac{4}{52}-\frac{2}{52}=\frac{28}{52}=\frac{7}{13}$$

FAQs (10)

1. What is addition theorem of probability? $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

2. What are mutually exclusive events? Events that cannot occur together.

3. What is probability of union of mutually exclusive events? Sum of their probabilities.

4. What is complementary event? Event opposite to given event.

5. What is probability of complementary events? $P(A)+P(A^{\mathrm{\prime }})=1$.

6. What are independent events? Events where occurrence of one does not affect the other.

7. What is probability of intersection of independent events? Product of their probabilities.

8. Can probability of union exceed 1? No, maximum is 1.

9. What is overlap in probability? Common outcomes in both events.

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

Conclusion

Exercise 14.2 has 10 solved questions and 10 FAQs that strengthen your understanding of the addition theorem of probability. This builds the foundation for advanced probability in Class 11 Maths.

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New Syllabus,Class 11 Maths Chapter 14 Probability – Exercise 14.2 NCERT