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For example, in tossing two coins together, if getting exactly one tail is considered an event
obtained, then the outcomes (TH) and (HT) are favourable outcomes of the event and the outcomes

(HH) and (TT) are unfavourable outcomes of the event.
Hence, getting HT or TH is called a favourable event or a successful event.

Here, TH is a simple event and HT alone is also a simple event.

Elementary and complementary events

An elementary event (E) is a simple event that has a single outcome, while a complementary event

is the non-occurrence of an event E ( ) , i.e., two events are said to be complementary when one
event occurs if and only if the other does not take place.

If n(E) elementary events are favourable to an event E out of n(S) elementary events (where 0 ≤
n(E) ≤ n(S)), then the complementary event or the number of elementary events ‘not E’ or E ( ) is
n(S) – n(E).

Probability of an Event

The probability of an event is a ratio that compares the number of favourable outcomes to the
number of possible outcomes. The chance of happening an event is called probability. Let E be
an event. Then, the probability of the event (E) is denoted by P(E) and is defined as follows:
E
Number of favourable outcomes n()
≤
P(E) = = , where 0 ≤ P(E) 1
S
Total number of possiblle outcomes n()
The probability that an event will happen is somewhere between 0 and 1. It can be shown on a
number line.

There is an equally
likely chance that the
event will happen
1 or 0.25 1 or 0.5 3 or 0.75

It is impossible 0 4 2 4 1 The event
for the event to is certain to
happen. happen
0% 25% 50% 75% 100%
Very unlikely Unlikely Likely Very Likely

In order to further strengthen our understanding of the concept of probability, let us deal with
some examples.

Example 8: A dice is thrown two times and the sum of the numbers 2 3 4 5 6 7
that appear on the dice is noted. Find the number of possible
outcomes. 3 4 5 6 7 8
4 5 6 7 8 9
Solution: When a dice is thrown two times, the sum of the numbers
that appear on the dice can be noted as follows. 5 6 7 8 9 10

Thus, the possible outcomes, S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. 6 7 8 9 10 11
\ n(S) = 11 7 8 9 10 11 12

111 Data Handling