NCERT Book Class 11 Maths Chapter 14 Probability

Chapter 14

PROBABILITY

vWhere a mathematical reasoning can be had, it is as great a folly to
make use of any other, as to grope for a thing in the dark, when
you have a candle in your hand. – JOHN ARBUTHNOT v

14.1 Event
We have studied about random experiment and sample space associated with an
experiment. The sample space serves as an universal set for all questions concerned
with the experiment.
Consider the experiment of tossing a coin two times. An associated sample space
is S = {HH, HT, TH, TT}.
Now suppose that we are interested in those outcomes which correspond to the
occurrence of exactly one head. We find that HT and TH are the only elements of S
corresponding to the occurrence of this happening (event). These two elements form
the set E = { HT, TH}
We know that the set E is a subset of the sample space S . Similarly, we find the
following correspondence between events and subsets of S.
Description of events Corresponding subset of ‘S’
Number of tails is exactly 2 A = {TT}
Number of tails is atleast one B = {HT, TH, TT}
Number of heads is atmost one C = {HT, TH, TT}
Second toss is not head D = { HT, TT}
Number of tails is atmost two S = {HH, HT, TH, TT}
Number of tails is more than two φ
The above discussion suggests that a subset of sample space is associated with
an event and an event is associated with a subset of sample space. In the light of this
we define an event as follows.
Definition Any subset E of a sample space S is called an event.