Probability RS Aggarwal Class8 ICSE Maths Goyal Brothers Prakashan Solutions Chapter27. We provide step by step Solutions of Exercise / lesson27 Graphical Representations of Statistical Data for ICSE Class8 RS Aggarwal Mathematics.
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Probability RS Aggarwal Class8 ICSE Maths Goyal Brothers Prakashan Solutions Chapter27
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Notes on Probability
Probability means possibility / Chance. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Definition of Probability:
Probability is defined as the numerical method of measuring uncertainty involved in a situation.
It is widely used in the study of mathematics, statistics, gambling, physical science, biological science, weather forecasting, finance etc. to draw conclusions.
Experiment:
An experiment is defined as an action or process that results in well defined outcomes
Formula for Probability
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Formula for Probability
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes
Random experiment:
An experiment, in which we know all the results, but cannot predict them, is called a random experiment.
Outcomes:
The possible results of an experiment are called the outcomes
Probability of an Event
A combination of outcomes is called an event
Assume an event E can occur in r ways out of a sum of n probable or possible equally likely ways. Then the probability of happening of the event or its success is expressed as
P(E) = r/n
The probability that the event will not occur or known as its failure is expressed as:
P(E’) = (nr)/n = 1(r/n)
E’ represents that the event will not occur.
Therefore, now we can say;
P(E) + P(E’) = 1
This means that the total of all the probabilities in any random test or experiment is equal to 1
Probability of an event = .
Probability Terms and Definition
Some of the important probability terms are discussed here:
Term  Definition  Example 

Sample Space  The set of all the possible outcomes to occur in any trial 

Sample Point  It is one of the possible results  In a deck of Cards:

Experiment or Trial  A series of actions where the outcomes are always uncertain.  The tossing of a coin, Selecting a card from a deck of cards, throwing a dice. 
Event  It is a single outcome of an experiment.  Getting a Heads while tossing a coin is an event. 
Outcome  Possible result of a trial/experiment  T (tail) is a possible outcome when a coin is tossed. 
Complimentary event  The nonhappening events. The complement of an event A is the event, not A (or A’)  Standard 52card deck, A = Draw a heart, then A’ = Don’t draw a heart 
Impossible Event  The event cannot happen 
Exe27 , Probability RS Aggarwal Class8 ICSE Maths Goyal Brothers Prakashan Solutions
Question 1:
A coin is tossed once. What is the probability of getting a head ?
Answer :
On tossing a coin once,
Number of possible outcome = 2
Similarly, favorable outcome getting a head = 1
So, P(E) = Number of favorable outcome/Number of all possible outcome = 1/2
Question 2:
A die is thrown once. What is the probability of getting :
(i) the number 4
(ii) an odd number ?
Answer :
A die has six numbers: 1, 2, 3, 4, 5, 6
Number of possible outcomes = 6
(i) the number = 4
Number of favorable outcome of getting a number 4 = 1
So, P(E) = Number of favorable outcome/Number of all possible outcome = 1/6
(ii) an odd number
Number of favorable outcomes = 3
So, P(E) = Number of favorable outcome/Number of all possible outcome = 3/6
= 1/2 Ans..
Question 3:
A die is thrown once, What is the probability of getting :
(i) a prime number
(ii) a number greater than 2
(iii) a number other than 2 and 5.
Answer :
A die has six numbers: 1, 2, 3, 4, 5, 6
Number of possible outcomes = 6
(i) a prime number
Number of favorable outcomes = a prime number = 1, 3, 5 which are 3 in numbers
So, P(E) = Number of favorable outcome/Number of all possible outcome = 3/6
= 1/2
(ii) Number of favorable outcome = greater than 2 i.e. four numbers 3, 4, 5 and 6
So, P(E) = Number of favorable outcome/Number of all possible outcome = 4/6
= 2/3
(iii) Number of favorable outcome = Number other than 2 and 5 i.e. 1, 3, 4, 6
So, P(E) = Number of favorable outcome/Number of all possible outcome = 4/6
= 2/3
Question 4:
Two coins are tossed simultaneously. Find the probability of getting :
(i) exactly one head
(ii) at least one tail
(iii) no tail
(iv) at most one head
Answer :
Total number of possible outcomes 4 ex. (HH), (HT), (TT) and (TH)
(i) Exactly one head
Possible number of favorable outcomes = 2
(ex. TH and HT)
So, P(E) = Number of favorable outcome/Number of all possible outcome = 2/4
= 1/2
(ii) At least one tail
Possible number of favorable outcomes = 3
Total number of possible outcomes = 4
So, P(E) = Number of favorable outcome/Number of all possible outcome = 3/4
(iii) No tails
Possible number of favorable outcomes = 1
Total number of possible outcomes = 4
So, P(E) = Number of favorable outcome/Number of all possible outcome = 1/4
(iv) At most one heads
Possible number of favorable outcomes = 3
(ex. TT, HT and TH)
Total numbers of possible outcomes = 4
So, P(E) = Number of favorable outcome/Number of all possible outcome = 3/4
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