RD Sharma Chapter 25 Class 9 Maths Exercise 25.1 Solutions is based on the Probability that consists of Various approaches to probability, essential terms like- Trial, elementary event & compound event, and Experimental approach to probability, etc. We have provided answers in a stepwise informative manner, which will help students solve questions faster to score well in the exam.
We have attached RD Sharma Chapter 25 Class 9 Maths Exercise 25.1 Solutions PDF for the reference that helps learners solve various kinds of questions based on Probability. Our experts prepare the PDF with the help of RD Sharma, Text Book, and Previous Year’s Question of Class 9.
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Solutions for Class 9 Maths Chapter 25 Probability Exercise 25.1
Important Definition RD Sharma Chapter 25 Class 9 Maths Exercise 25.1 Solutions
The probability remains anywhere between 0 and 1. Probability being 0 signifies that the event will be impossible, and when the probability is 1, it signifies a specific event. Below are some fundamental terms one should understand before going further.
Various Approaches to Probability
There are three modes of assigning probabilities for the events called classical approach, relative-frequency approach, and subjective approach.
Experimental or empirical; Approach to Probability
Experimental or empirical probability is the probability made following past data. Alternatively, it explains the possibility of an event happening as per past data.
Experiment or Trial
This is a set of actions in which the results don’t remain certain. By experiment or trial in the matter of probability, we determine a random experiment unless otherwise defined.
Each trial occurs in one or more outcomes.
Examples-
- Tossing four coins.
- Picking three balls from a bag carrying ten balls, four of which are blue.
- Rolling a dice.
The Trial, Elementary Event, and Compound Event
Any specific performance of a randomly done experiment is called a trial.
The elementary event often referred to as atomic event or sample point) is something that contains explicitly one result in the sample space. As per set theory terms, an elementary event is a singleton.
A compound event represents two or multiple events, which comes with two or multiple results.
Event or Outcome
This is the precise result of an experiment means that something that occurs. It is a result that is produced by some former action.
Note-
It is not necessary that the alphabets used for naming events are to be considered sequentially. They can be considered in any order. Although, consecutively taking them would aid understanding.
Examples-
The experiment from “Tossing a Coin”, which have two possible events/ outcomes-
- Event A- Getting Head
- Event B- Getting Tail
The experiment from “Throwing a Dice”, which have six events/ outcomes-
- Event A- Showing up one (1) on its face.
- Event B- Showing up one (2) on its face.
- Event C- Showing up one (3) on its face.
- Event D- Showing up one (4) on its face.
- Event E- Showing up one (5) on its face.
- Event F- Showing up one (6) on its face.
Sample Space
The collection of entire probable results that can happen in any trial is called the sample space.
Sample Space is formed through Sample Points. Similarly, the sample point can be any of the probable results.
Examples Related to the RD Sharma Chapter 25 Class 9 Maths Exercise 25.1 Solutions
Ques- A coin is rolled 1000 times with the below sequence.
Head- 455
Tail- 545
Compute the probability of each event.
Solution-
The coin is rolled 1000 times, which means, number of trials is 1000 (thousand).
Let us consider the event of getting head and getting tail to be A and B.
No. of favorable outcome = No. of trials in which the A happens = 455
So, Probability of A = (Number of favorable outcomes) / (Total no. of trials)
F(A) = 455/1000 = 0.455
Similarly,
No. of favorable outcome = No. of trials in which the B happens = 545
Probability of the event getting a tail, F(B) = 545/1000 = 0.545
Ques- Two coins are tossed simultaneously 500 times with the below frequencies of different outcomes:
Two heads- 95 times
One tail- 290 times
No head- 115 times
Get the probability of occurrence of each of these events.
Solution-
We know that the Probability of any event = (No. of favorable outcome)/ (Total no. of trials)
Total no. of cases = 95 + 290 + 115 = 500
Now,
F(Getting two heads) = 95/500 = 0.19
F(Getting one tail) = 290/500 = 0.58
F(Getting no head) = 115/500 = 0.23
Ques- In the cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that on a ball played-
(a) He hits boundary (b) He does not hit a boundary.
Solution-
Total no of balls played by the player = 30
No of times he hits the boundary = 6
N0 of times he does not hit the boundary = 30 – 6 = 24
As we know that, the Probability of an event = (No. of Favorable outcomes)/ (Total No. of outcomes)
Now,
(a) Probability (he hits boundary) = (No. of times he hit a boundary)/ (Total no. of balls he played)
= 6/30 = 1/5
(b) Probability that the batsman doesn’t hit a boundary = 24/30 = 4/5.
Frequently Asked Questions (FAQs) of RD Sharma Chapter 25 Class 9 Maths Exercise 25.1 Solutions
Ques 1- What does a result of an experiment is called?
Ans- An sample point is the result of the experiment. The collection of all possible sample points or outcomes of an experiment is known as the Sample Space. An event is the subset of a sample space.
Ques 2- What is a random experiment with an example?
Ans- A Random Experiment is a trial or observation repeated many times under the equivalent conditions.
Examples- Tossing a coin. The observation can generate two possible results, heads or tails.