Class 10 Maths Chapter 14 Probability – Exercise 14.1 NCERT Solutions

Introduction

Exercise 14.1 introduces the concept of probability based on equally likely outcomes. Probability measures the chance of occurrence of an event and is widely used in real‑life situations like games, weather forecasting, and risk analysis.

Formula Used

For an event $E$:

$$$$P(E)=Number of favourable outcomesTotal number of outcomes

Where:

• $P(E)$ = probability of event $E$

• Favourable outcomes = outcomes that satisfy event $E$

• Total outcomes = all possible outcomes

NCERT Questions with Solutions (10)

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

$$P(\text{Head})=\frac{1}{2}$$

Q2. A die is thrown once. Find probability of getting number greater than 4. Favourable outcomes = $\{5,6\}$, Total = 6

$$P=\frac{2}{6}=\frac{1}{3}$$

Q3. A die is thrown once. Find probability of getting even number. Favourable outcomes = $\{2,4,6\}$, Total = 6

$$P=\frac{3}{6}=\frac{1}{2}$$

Q4. A coin is tossed twice. Find probability of getting two heads. Total outcomes = $\{HH,HT,TH,TT\}$, Favourable = $\{HH\}$

$$P=\frac{1}{4}$$

Q5. A coin is tossed twice. Find probability of getting at least one head. Favourable outcomes = $\{HH,HT,TH\}$, Total = 4

$$P=\frac{3}{4}$$

Q6. A die is thrown once. Find probability of getting prime number. Prime outcomes = $\{2,3,5\}$, Total = 6

$$P=\frac{3}{6}=\frac{1}{2}$$

Q7. A die is thrown once. Find probability of getting composite number. Composite outcomes = $\{4,6\}$, Total = 6

$$P=\frac{2}{6}=\frac{1}{3}$$

Q8. A coin is tossed once. Find probability of getting tail.

$$P(\text{Tail})=\frac{1}{2}$$

Q9. A die is thrown once. Find probability of getting odd number. Odd outcomes = $\{1,3,5\}$, Total = 6

$$P=\frac{3}{6}=\frac{1}{2}$$

Q10. A coin is tossed thrice. Find probability of getting exactly two heads. Total outcomes = 8, Favourable = $\{HHT,HTH,THH\}$

$$P=\frac{3}{8}$$

FAQs (10)

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

2. Formula for probability?

$$P(E)=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$$

3. Range of probability? Between 0 and 1.

4. What is certain event? Probability = 1.

5. What is impossible event? Probability = 0.

6. Can probability be negative? No.

7. What is equally likely outcome? Outcomes with equal chance of occurrence.

8. Examples of probability in daily life? Tossing coin, rolling die, weather forecast.

9. Difference between theoretical and experimental probability? Theoretical = formula based, Experimental = based on trials.

10. Why is this exercise important? Builds foundation for advanced probability concepts.

Conclusion

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

Visit: www.fuzymathacademy.com

New Syllabus- Class 10 Maths Chapter 14 Probability – Exercise 14.1 NCERT Solutions