Probability can range in between 0 to 1, where 0 probability means the event to be an impossible and probability 1 indicates the certain event. Before we get into depth, we should know some basic terms as listed below:
Sample Space- The set of all the possible outcomes to occur in any trial is known as sample space.
Examples- Tossing a coin, Sample Space (S) = {H,T} and Rolling a die, Sample Space (S) = {1,2,3,4,5,6}
Sample Space is made up of Sample Points. Whereas, sample point is one of the possible results. For example, in a deck of cards, 3 of diamond is a sample point
Experiment or Trial- It is a series of action where the outcomes are always uncertain.
Event- It is a single outcome of an experiment.
Learn about the concept in depth and how to solve problems through RD Sharma solutions that are provided at BYJU’S. It acts as perfect self-help guidance for students without any doubt.
Download PDF of RD Sharma Solutions for Class 9 Maths Chapter 25 Probability Exercise 25.1
Access Answers to Maths RD Sharma Class 9 Chapter 25 Probability Exercise 25.1 Page number 25.13
Exercise 25.1 Page No: 25.13
Question 1: A coin is tossed 1000 times with the following sequence:
Head: 455, Tail: 545
Compute the probability of each event.
Solution:
Coin is tossed 1000 times, which means, number of trials are 1000.
Let us consider, event of getting head and event of getting tail be E and F respectively.
Number of favorable outcome = Number of trials in which the E happens = 455
So, Probability of E = (Number of favorable outcome) / (Total number of trials)
P(E) = 455/1000 = 0.455
Similarly,
Number of favorable outcome = Number of trials in which the F happens = 545
Probability of the event getting a tail, P(F) = 545/1000 = 0.545
Question 2: Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One tail: 290 times
No head : 115 times
Find the probability of occurrence of each of these events.
Solution:
We know that, Probability of any event = (Number of favorable outcome) / (Total number of trials)
Total number of trials = 95 + 290 + 115 = 500
Now,
P(Getting two heads) = 95/500 = 0.19
P(Getting one tail) = 290/500 = 0.58
P(Getting no head) = 115/500 = 0.23
Question 3: Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:
Outcome |
No head |
One head |
Two heads |
Three heads |
Frequency |
14 |
38 |
36 |
12 |
If the three coins are simultaneously tossed again, compute the probability of:
(i) 2 heads coming up
(ii) 3 heads coming up
(iii) At least one head coming up
(iv) Getting more heads than tails
(v) Getting more tails than heads
Solution:
We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)
In this case, total numbers of outcomes = 100.
(i) Probability of 2 Heads coming up = 36/100 = 0.36
(ii) Probability of 3 Heads coming up = 12/100 = 0.12
(iii) Probability of at least one head coming up = (38+36+12) / 100 = 86/100 = 0.86
(iv) Probability of getting more Heads than Tails = (36+12)/100 = 48/100 = 0.48
(v) Probability of getting more tails than heads = (14+38) / 100 = 52/100 = 0.52
Question 4: 1500 families with 2 children were selected randomly, and the following data were recorded:
If a family is chosen at random, compute the probability that it has:
(i) No girl (ii) 1 girl (iii) 2 girls (iv) At most one girl (v) More girls than boys
Solution:
We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)
In this case, total numbers of outcomes = 211 + 814 + 475 = 1500.
(Here, total numbers of outcomes = total number of families)
(i) Probability of having no girl = 211/1500 = 0.1406
(ii) Probability of having 1 girl = 814/1500 = 0.5426
(iii) Probability of having 2 girls = 475/1500 = 0.3166
(iv) Probability of having at the most one girl = (211+814) /1500 = 1025/1500 = 0.6833
(v) Probability of having more girls than boys = 475/1500 = 0.31
Question 5: In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that on a ball played:
(i) He hits boundary (ii) He does not hit a boundary.
Solution:
Total number of balls played by a player = 30
Number of times he hits a boundary = 6
Number of times he does not hit a boundary = 30 â€“ 6 = 24
We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)
Now,
(i) Probability (he hits boundary) = (Number of times he hit a boundary) / (Total number of balls he played)
= 6/30 = 1/5
(ii) Probability that the batsman does not hit a boundary = 24/30 = 4/5
Question 6: The percentage of marks obtained by a student in monthly unit tests are given below:
Find the probability that the student gets
(i) More than 70% marks
(ii) Less than 70% marks
(iii) A distinction
Solution:
Total number of unit tests taken = 5
We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)
(i) Number of times student got more than 70% = 3
Probability (Getting more than 70%) = 3/5 = 0.6
(ii) Number of times student got less than 70% = 2
Probability (Getting less than 70%) = 2/5 = 0.4
(iii) Number of times student got a distinction = 1
[Marks more than 75%]Probability (Getting a distinction) = 1/5 = 0.2
Question 7: To know the opinion of the students about Mathematics, a survey of 200 students were conducted. The data was recorded in the following table:
Find the probability that student chosen at random:
(i) Likes Mathematics (ii) Does not like it.
Solution:
Total number of students = 200
Students like mathematics = 135
Students dislike Mathematics = 65
We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)
(i) Probability (Student likes mathematics) = 135/200 = 0.675
(ii) Probability (Student does not like mathematics) = 65/200 = 0.325
Access other exercise solutions of Class 9 Maths Chapter 25 Probability
RD Sharma Solutions for Class 9 Maths Chapter 25 Exercise 25.1
Class 9 Maths Chapter 25 Probability Exercise 25.1 is based on following topics:
- Various approaches to probability
- Experimental or empirical; approach to probability
- Some important terms: Trial, elementary event and compound event