Class 10 Math Chapter 14 Probability – Complete NCERT Solutions

Introduction

Probability is the branch of mathematics that deals with the likelihood of events. In Class 9, you studied experimental probability. In Class 10, we focus on theoretical probability, which is based on equally likely outcomes. Probability is widely used in science, economics, genetics, and everyday decision‑making.

Key Formula

The probability of an event $E$ is defined as:

$$\mathrm{<b><span\; style="font-family:\; verdana;">P</span></b>}<b><span\; style="font-family:\; verdana;">(</span></b>\mathrm{<b><span\; style="font-family:\; verdana;">E</span></b>}<b><span\; style="font-family:\; verdana;">)</span></b><b><span\; style="font-family:\; verdana;">=</span></b>\frac{\text{<b><span style="font-family: verdana;">Number of favourable outcomes</span></b>}}{\text{<b><span style="font-family: verdana;">Total number of possible outcomes</span></b>}}$$

• Probability of a sure event = 1

• Probability of an impossible event = 0

• For any event $E$: $0\le P(E)\le 1$

• Complementary events: $P(E)+P(\bar{E})=1$

Solved Examples from NCERT

Example 1: Tossing a coin once.

• P(Head) = 1/2, P(Tail) = 1/2.

Example 2: Bag with red, blue, yellow balls.

• P(Yellow) = 1/3, P(Red) = 1/3, P(Blue) = 1/3.

Example 3: Throwing a die.

• P(Number > 4) = 2/6 = 1/3.

• P(Number ≤ 4) = 4/6 = 2/3.

Example 4: Drawing a card from 52 cards.

• P(Ace) = 4/52 = 1/13.

• P(Not Ace) = 48/52 = 12/13.

Example 5: Probability of Sangeeta winning tennis match = 0.62.

• P(Reshma winning) = 1 – 0.62 = 0.38.

Example 9: Tossing two coins.

• P(At least one head) = 3/4.

Example 13: Throwing two dice.

• P(Sum = 8) = 5/36.

• P(Sum = 13) = 0.

• P(Sum ≤ 12) = 1.

Exercise Solutions (Step by Step)

Each NCERT exercise question is solved with clear steps. For example:

Exercise 14.1 (8): Bag with 3 red and 5 black balls.

• P(Red) = 3/8.

• P(Not Red) = 5/8.

(And similarly for all exercise questions – each solved step by step.)

15 FAQs with Solutions

1. Q: What is probability? A: Measure of likelihood of an event.

2. Q: Formula for probability? A: $P(E)=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$.

3. Q: Probability of impossible event? A: 0.

4. Q: Probability of sure event? A: 1.

5. Q: Probability range? A: Between 0 and 1.

6. Q: What are complementary events? A: Events E and not E, with sum of probabilities = 1.

7. Q: Probability of drawing ace from 52 cards? A: 1/13.

8. Q: Probability of drawing red card from 52 cards? A: 26/52 = 1/2.

9. Q: Probability of getting prime number on die? A: 3/6 = 1/2.

10. Q: Probability of getting odd number on die? A: 3/6 = 1/2.

11. Q: Probability of getting king of red colour? A: 2/52 = 1/26.

12. Q: Probability of drawing face card? A: 12/52 = 3/13.

13. Q: Probability of drawing queen of diamonds? A: 1/52.

14. Q: Probability of getting sum 8 on two dice? A: 5/36.

15. Q: Probability of Hanif losing coin toss game (3 tosses)? A: 6/8 = 3/4.

Conclusion

Probability is a powerful tool to predict outcomes in uncertain situations. By mastering theoretical probability, you can solve NCERT problems and apply them to real‑life contexts like games, cards, dice, and everyday decisions.

visit: www.fuzymathacademy.com