RD Sharma Solutions for Class 9 Maths Chapter 25 Probability
Here you’ll find solutions for Chapter 25 of Class 9 Maths from RD Sharma, which covers the topic of Probability. Probability tells us how likely it is for a certain event to happen. It is shown as a number between 0 and 1.
A basic example is tossing a coin. A coin has two sides – heads and tails. So, there are only two possible results. The chance of getting heads is the same as the chance of getting tails, which is 1 out of 2, or ½.
The step-by-step answers in the RD Sharma Solutions help students understand the topic better and gain confidence in solving different types of questions easily.
What is Probability?
Probability is the chance that something will happen. Some events are not easy to predict for sure, but we can estimate how likely they are. For example, we can’t say for sure what number will come up when a die is rolled, but we can talk about the chances of each number.
To understand Probability and other Maths topics better, keep practicing with RD Sharma Class 9 Solutions. These are made by subject experts and follow the CBSE syllabus, helping students do well in exams.
RD Sharma Solution for Class 9 Chapter 25 - Download PDF
Here are the RD Sharma Solutions Class 9 Maths Chapter 25 Probability Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
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RD Sharma Solution for Class 9 Chapter 25 - Question with Answers
Certainly! Here are 30 practice questions with answers based on Chapter 25 – Probability from RD Sharma Class 9 Maths. These questions cover various concepts such as experimental probability, theoretical probability, and real-life applications.
1. A coin is tossed 1000 times, resulting in 455 heads and 545 tails. Find the probability of getting:
- (i) a head
Answer: Probability of head = 455 / 1000 = 0.455 - (ii) a tail
Answer: Probability of tail = 545 / 1000 = 0.545
2. Two coins are tossed simultaneously 500 times with the following outcomes:
- Two heads: 95 times
- One tail: 290 times
- No head: 115 times
Find the probability of occurrence of each event.
- (i) Two heads
Answer: 95 / 500 = 0.19 - (ii) One tail
Answer: 290 / 500 = 0.58 - (iii) No head
Answer: 115 / 500 = 0.23
3. Three coins are tossed simultaneously 100 times with the following frequencies:
- 3 heads: 12 times
- 2 heads: 36 times
- 1 head: 38 times
- No head: 14 times
Find the probability of:
- (i) 2 heads
Answer: 36 / 100 = 0.36 - (ii) 3 heads
Answer: 12 / 100 = 0.12 - (iii) At least one head
Answer: (38 + 36 + 12) / 100 = 86 / 100 = 0.86 - (iv) More heads than tails
Answer: (36 + 12) / 100 = 48 / 100 = 0.48 - (v) More tails than heads
Answer: (14 + 38) / 100 = 52 / 100 = 0.52
4. In a cricket match, a batsman hits a boundary 6 times out of 30 balls. Find the probability that on a ball played:
- (i) He hits a boundary
Answer: 6 / 30 = 0.2 - (ii) He does not hit a boundary
Answer: (30 - 6) / 30 = 24 / 30 = 0.8
5. A die is thrown 100 times with the following outcomes:
- 1: 14 times
- 2: 16 times
- 3: 15 times
- 4: 20 times
- 5: 18 times
- 6: 17 times
Find the probability of each outcome.
- (i) Getting a 1
Answer: 14 / 100 = 0.14 - (ii) Getting a 2
Answer: 16 / 100 = 0.16 - (iii) Getting a 3
Answer: 15 / 100 = 0.15 - (iv) Getting a 4
Answer: 20 / 100 = 0.20 - (v) Getting a 5
Answer: 18 / 100 = 0.18 - (vi) Getting a 6
Answer: 17 / 100 = 0.17
6. A bag contains 4 white balls and some red balls. If the probability of drawing a white ball is 1/5, find the number of red balls.
Answer: Let the number of red balls be x.
Total balls = 4 (white) + x (red)
Probability of white ball = 4 / (4 + x) = 1 / 5
Cross-multiplying: 5 × 4 = 4 + x
20 = 4 + x
x = 16
Number of red balls = 16
7. A die is thrown 100 times. If the probability of getting an even number is 2/5, how many times is an odd number obtained?
Answer: Probability of even number = 2/5
Number of times even number occurs = (2/5) × 100 = 40
Number of times odd number occurs = 100 - 40 = 60
Odd number obtained 60 times
8. The blood groups of 30 students are recorded as follows:
- A: 9 students
- B: 6 students
- AB: 3 students
- O: 12 students
Find the probability that a student chosen at random has:
- (i) Blood group A
Answer: 9 / 30 = 0.3 - (ii) Blood group B
Answer: 6 / 30 = 0.2 - (iii) Blood group AB
Answer: 3 / 30 = 0.1 - (iv) Blood group O
Answer: 12 / 30 = 0.4
9. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights (in kg):
4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
Find the probability that a randomly chosen bag contains more than 5 kg of flour.
Answer: Bags with more than 5 kg: 5.05, 5.08, 5.03, 5.06, 5.08, 5.04, 5.07 (7 bags)
Total bags = 11
Probability = 7 / 11 ≈ 0.636
Probability ≈ 0.636
10. The birth months of 40 students are recorded. If 6 students were born in August, find the probability that a student chosen at random was born in August.
Answer: 6 / 40 = 0.15
Probability = 0.15
11. A number is selected at random from the numbers 1 to 20. What is the probability that the selected number is a multiple of 3?
Answer:
Multiples of 3 between 1 and 20 = 3, 6, 9, 12, 15, 18 → 6 numbers
Total outcomes = 20
Probability = 6 / 20 = 0.3
12. What is the probability of getting a prime number when a die is thrown?
Answer:
Prime numbers between 1 and 6 = 2, 3, 5 → 3 numbers
Total outcomes = 6
Probability = 3 / 6 = 0.5
13. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a king.
Answer:
Number of kings = 4
Total cards = 52
Probability = 4 / 52 = 1/13
14. A bag contains 3 red, 5 blue, and 2 green balls. One ball is drawn at random. Find the probability that it is:
- (i) Red
Answer: 3 / 10 = 0.3 - (ii) Blue
Answer: 5 / 10 = 0.5 - (iii) Green
Answer: 2 / 10 = 0.2
15. A letter is chosen at random from the word “MATHEMATICS”. What is the probability that it is:
- (i) A vowel
Vowels: A, E, A, I → 4 vowels
Total letters = 11
Probability = 4 / 11 ≈ 0.364 - (ii) A consonant
Answer: 7 / 11 ≈ 0.636
16. A spinner has numbers 1 to 5. What is the probability of getting:
- (i) An odd number
Odd numbers = 1, 3, 5 → 3 outcomes
Probability = 3 / 5 = 0.6 - (ii) A number less than 4
Numbers < 4 = 1, 2, 3 → 3 outcomes
Probability = 3 / 5 = 0.6
17. What is the probability of getting a number divisible by 2 or 3 from numbers 1 to 15?
Answer:
Multiples of 2 or 3 = 2, 3, 4, 6, 8, 9, 10, 12, 14, 15 → 10 numbers
Total numbers = 15
Probability = 10 / 15 = 2/3
18. A bag has 7 red, 3 green, and 5 yellow balls. Find the probability of not drawing a green ball.
Answer:
Green balls = 3
Total balls = 15
Not green = 15 - 3 = 12
Probability = 12 / 15 = 0.8
19. The outcomes of a dice game are recorded as:
- 1 appeared 5 times
- 2 appeared 7 times
- 3 appeared 10 times
- 4 appeared 13 times
- 5 appeared 9 times
- 6 appeared 6 times
Find the probability of getting a 4.
Answer:
Total throws = 5 + 7 + 10 + 13 + 9 + 6 = 50
Frequency of 4 = 13
Probability = 13 / 50 = 0.26
20. In a survey of 100 students, 60 like Maths, 40 like Science. If one student is selected randomly, find the probability that the student:
- (i) Likes Maths
Answer: 60 / 100 = 0.6 - (ii) Likes Science
Answer: 40 / 100 = 0.4
21. A coin is tossed once. What is the probability of getting a head?
Answer:
Probability = 1 / 2 = 0.5
22. Find the probability of drawing a vowel from the English alphabet.
Answer:
Vowels = A, E, I, O, U → 5
Total letters = 26
Probability = 5 / 26 ≈ 0.192
23. A die is thrown. What is the probability of getting a number greater than 4?
Answer:
Numbers > 4 = 5, 6 → 2 outcomes
Probability = 2 / 6 = 1/3
24. From numbers 1 to 50, find the probability of selecting a number that is a perfect square.
Answer:
Perfect squares = 1, 4, 9, 16, 25, 36, 49 → 7 numbers
Total = 50
Probability = 7 / 50 = 0.14
25. A girl throws a die. What is the probability that she gets an even number?
Answer:
Even numbers = 2, 4, 6 → 3 outcomes
Probability = 3 / 6 = 0.5
26. What is the probability of selecting a consonant from the word “PROBABILITY”?
Answer:
Total letters = 11
Vowels = O, A, I, I → 4 vowels
Consonants = 7
Probability = 7 / 11 ≈ 0.636
27. A card is drawn from a deck. Find the probability it is:
- (i) A black card
Answer: 26 / 52 = 0.5 - (ii) A red king
Answer: 2 / 52 = 1/26
28. A number is selected at random from 1 to 100. Find the probability that it is divisible by 5.
Answer:
Numbers divisible by 5 = 20
Probability = 20 / 100 = 0.2
29. A coin is tossed 400 times. Heads appeared 224 times. What is the probability of getting a tail?
Answer:
Tails = 400 - 224 = 176
Probability = 176 / 400 = 0.44
30. A student guesses the answer to a true-false question. What is the probability that the answer is correct?
Answer:
Correct guess = 1 out of 2
Probability = 1/2 or 0.5
RD Sharma Solutions for Class 9 Maths Chapter 25 FAQs
What is the main topic covered in Chapter 25 of RD Sharma Class 9 Maths?
Chapter 25 of RD Sharma Class 9 covers the topic of Probability, which is the measure of the likelihood or chance of an event occurring.
Why is Probability important for Class 9 students?
Probability is important because it introduces students to real-life applications of mathematics in uncertain situations like games, weather forecasting, and risk analysis. It also lays the foundation for higher-level topics in statistics and data science.
What is the formula to calculate probability?
The basic formula is: Probability of an event (P) = (Number of favorable outcomes) / (Total number of outcomes)
What are some real-life examples of probability?
Examples include:
Tossing a coin (chance of heads or tails)
Rolling a die (getting a specific number)
Drawing a card from a deck
Predicting rain using weather forecasts
How many questions are there in Chapter 25 of RD Sharma?
The chapter usually contains multiple exercises with around 30 to 40 questions including theory and practical problems based on data interpretation and events.
Are RD Sharma solutions for Probability enough for CBSE Class 9 exams?
Yes, RD Sharma provides detailed and concept-based solutions that are more than sufficient to prepare for school-level exams. They follow the CBSE curriculum strictly and provide ample practice.