Page 268 - ICSE Math 8

The probability of a sure event is always one (1), i.e., P(sure event) = 1. the probability of an imposible
event is zero(0), i.e., P(impossible event) = 0.
(iv) Sample space: A collection of all possible outcomes of an experiment is called sample space. For example,
all the possible events of a throwing die, i.e., 1, 2, 3, 4, 5 and 6 are collectively called the sample space
of this experiment. Thus, the sample space of rolling a die is {1, 2, 3, 4, 5, 6}.
(v) Favourable event: An outcome is said to be favourable to a compound event A, if the event A consists of
the outcome as one of its sample points.
Consider the random experiment of throwing a pair of dice and the compound event A defined by “Getting
6 as the sum”. Event A occurs if we get any one of the following outcomes:
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
So, there are 5 outcomes favourable to event A.

(vi) Negation of an event: Corresponding to every event A associated with a random experiment, an event “not
A” occurs when A does not occur. The event “not A” is called the negation of the event A and is denoted
by A . For example, while tossing a coin, negation head is appearance of a tail.

Event A occurs if A does not occur and vice versa.

Tossing one, two or three coins
Consider an example of an experiment of tossing a coin. The two possible outcomes are
either head (H) or tail (T).
Let’s now toss two coins simultaneously. There can be the following possible outcomes:
HH, HT, TH, TT.

Let’s now toss three coins simultaneously. There can be the following possible outcomes:
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.

n
If n coins are tossed simultaneously, then the total possible outcomes are 2 .

Throwing a die twice or two dice simultaneously

Consider a random experiment of throwing an unbiased die. The possible outcomes are: 1, 2, 3, 4, 5 or 6. So,
the six outcomes are:
Let’s now throw two dice simultaneously (or a single die two times). The possible outcomes are:

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
So, there are 36 outcomes associated with this random experiment.

n
If n dice are thrown simultaneously, the total possible outcomes are 6 .

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