Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q1. A coin is tossed 1000 times with the following sequence: Head: 455, Tail = :545. Compute the probability of each event

Answer: It is given that the coin is tossed 1000 times. The number of trials is 1000

Let us denote the event of getting head and of getting tails be E and F respectively. Then

Number of trials in which the E happens = 455

So, Probability of  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Similarity, the probability of the event getting a tail  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics


Q2. Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:

TWO HEADS: 95 times

ONE HEADS: 290 times

NO HEADS: 115 times

Find the probability of occurrence of each of these events

Answer:

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q3. Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:

OUTCOMENO HEADONE HEADTWO HEADTHREE HEAD
FREQUENCY14383612

 

 If the three coins are tossed simultaneously again, compute the probability of:

1.  heads coming up

2. heads coming up

3. At least one Head coming up

4. Getting more Tails than Heads 

5. Getting more heads than tails

ANS:

1: Probability of 2 Heads coming up  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

2. Probability of 3 Heads coming up  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

3. Probability of at least one head coming up  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

4. Probability of getting more Heads than Tails  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

5. Probability of getting more tails than heads RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q4. 1500 families with 2 children were selected randomly, and the following data were recorded:

No of girls in a family012
No of girls211814475


If a family is chosen at random, compute the probability that it has:

1. No girl

2. 1 girl

3. 2 girls

4. At most one girl

5. More girls than boys


Answer

1. Probability of having no girl in a family RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

2. Probability of having 1 girl in a family  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

3. Probability of having 2 girls in a family RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

4. Probability of having at the most one girl  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

5. Probability of having more girls than boys  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q5. In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that:

1. He hit a boundary

2. He did not hit a boundary.

Answer

Number of times the batsman hits a boundary= 6

Total number of balls played= 30

Number of times the batsman did not hit a boundary= 30-6 = 24

1. Probability that the batsman hits a boundary  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

= 6/30

= 1/5


2. Probability that the batsman does not hit a boundary

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

= 24/30

= 4/5


Q6. The percentage of marks obtained by a student in the monthly unit tests are given below:

UNIT TESTIIIIIIIVV
PERCENTAGE OF MARK OBTAINED6971736876


Find the probability that the student gets

1. More than 70% marks

2. Less than 70% marks

3. A distinction

Answer:

1: Let E be the event of getting more than 70% marks

No of times E happens=3

Probability(Getting more than 70%)  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

2. Let F be the event of getting less than 70% marks

No of times F happen = 2

Probability(Getting less than 70%) RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

3. Let G be the event of getting distinction

No of times G happen = 1

Probability(Getting distinction) = RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q7. To know the opinion of the students about Mathematics, a survey of 200 students were conducted. The data was recorded in the following table

Opinion  LikeDislike
Number of students  13565

 

Find the probability that student chosen at random:

1. Likes Mathematics

2. Does not like it.

Answer

1. Probability that a student likes mathematics RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

2. Probability that a student does not like mathematics  RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

The document RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on RD Sharma Solutions Ex-25.1, (Part - 1), Probability, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics

1. What is the importance of studying probability in Class 9 Mathematics?
Ans. Studying probability in Class 9 Mathematics is important as it helps students understand the concept of uncertainty and randomness in real-life situations. Probability allows us to make predictions and analyze the likelihood of events occurring. It also plays a crucial role in various fields such as statistics, economics, and science.
2. What are the basic concepts of probability?
Ans. The basic concepts of probability include experiments, outcomes, sample space, events, and probability of an event. An experiment is a process that produces some outcomes. The set of all possible outcomes is called the sample space. An event is a subset of the sample space. Probability of an event is the measure of the likelihood of that event occurring and is represented by a number between 0 and 1.
3. How do you calculate the probability of an event?
Ans. The probability of an event can be calculated by dividing the number of favorable outcomes by the number of total outcomes in the sample space. It is represented as P(E) = Number of favorable outcomes / Number of total outcomes. The probability can also be represented as a fraction, decimal, or percentage.
4. What is the difference between experimental probability and theoretical probability?
Ans. Experimental probability is based on actual observations and experiments, where the probability of an event is determined by conducting the experiment multiple times and counting the favorable outcomes. Theoretical probability, on the other hand, is based on mathematical calculations and is determined by analyzing the sample space and the likelihood of each outcome.
5. How is probability used in real-life situations?
Ans. Probability is used in various real-life situations such as weather forecasting, risk analysis, gambling, insurance, and medical research. It helps in making informed decisions by analyzing the likelihood of certain events occurring. For example, probability is used to calculate the chances of rain, the risk associated with investments, or the effectiveness of a new drug in medical trials.
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