Class 12 Maths Chapter 13 Probability – Exercise 13.2 NCERT Solutions

Introduction

Exercise 13.2 focuses on addition theorem of probability and the concept of mutually exclusive and exhaustive events. Students learn how to calculate probabilities of union of events, apply the addition rule, and solve problems involving overlapping events. This exercise builds the foundation for conditional probability and Bayes’ theorem.

Key Concepts

1. Addition Theorem: For any two events $A$ and $B$,

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

2. Mutually Exclusive Events: If $A\cap B=\mathrm{\varnothing }$, then

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

3. Exhaustive Events: Events covering entire sample space.

4. Complement Rule:

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

Students Frequently Make Mistakes

• Forgetting to subtract intersection term in addition theorem.

• Misinterpreting mutually exclusive events.

• Errors in identifying exhaustive events.

• Skipping complement rule.

• Confusing union with intersection.

NCERT Questions with Step‑by‑Step Solutions (10)

Q1. If $P(A)=\frac{1}{4},P(B)=\frac{1}{2},P(A\cap B)=\frac{1}{8}$, find $P(A\cup B)$.

$$P(A\cup B)=\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=\frac{5}{8}$$

Q2. If $P(A)=0.3,P(B)=0.4,P(A\cap B)=0.2$, find $P(A\cup B)$.

$$P(A\cup B)=0.3+0.4-0.2=0.5$$

Q3. If $P(A)=0.5,P(B)=0.6,P(A\cap B)=0.3$, find $P(A\cup B)$.

$$P(A\cup B)=0.5+0.6-0.3=0.8$$

Q4. If $P(A)=0.2,P(B)=0.3,P(A\cap B)=0.1$, find $P(A\cup B)$.

$$P(A\cup B)=0.2+0.3-0.1=0.4$$

Q5. If $P(A)=0.4,P(B)=0.5,P(A\cap B)=0.2$, find $P(A\cup B)$.

$$P(A\cup B)=0.4+0.5-0.2=0.7$$

Q6. If $P(A)=0.6,P(B)=0.7,P(A\cap B)=0.4$, find $P(A\cup B)$.

$$P(A\cup B)=0.6+0.7-0.4=0.9$$

Q7. If $P(A)=0.3,P(B)=0.5,P(A\cap B)=0.2$, find $P(A\cup B)$.

$$P(A\cup B)=0.3+0.5-0.2=0.6$$

Q8. If $P(A)=0.25,P(B)=0.35,P(A\cap B)=0.15$, find $P(A\cup B)$.

$$P(A\cup B)=0.25+0.35-0.15=0.45$$

Q9. If $P(A)=0.4,P(B)=0.3,P(A\cap B)=0.1$, find $P(A\cup B)$.

$$P(A\cup B)=0.4+0.3-0.1=0.6$$

Q10. If $P(A)=0.5,P(B)=0.4,P(A\cap B)=0.2$, find $P(A\cup B)$.

$$P(A\cup B)=0.5+0.4-0.2=0.7$$

FAQs (10)

FAQ1. What is addition theorem of probability? $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

FAQ2. What are mutually exclusive events? Events that cannot occur together.

FAQ3. What are exhaustive events? Events covering entire sample space.

FAQ4. What is complement rule? $P(A^{\mathrm{\prime }})=1-P(A)$.

FAQ5. What is probability of union of two events? Sum of probabilities minus intersection.

FAQ6. What is probability of mutually exclusive events? $P(A\cup B)=P(A)+P(B)$.

FAQ7. What is probability of exhaustive events? Sum of probabilities = 1.

FAQ8. What is intersection of events? Common outcomes of events.

FAQ9. What is union of events? All outcomes belonging to either event.

FAQ10. Why is Exercise 13.2 important? It builds foundation for conditional probability and Bayes’ theorem.

Conclusion

Exercise 13.2 has 10 solved questions and 10 FAQs that strengthen your understanding of addition theorem of probability and mutually exclusive events. This builds the foundation for advanced probability concepts in Class 12 Maths.

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