Page 332 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 26: Theory of Probability: Introduction and Uses

Examples: (i) In case of tossing a die, the set of six possible outcomes, i.e., 1, 2, 3, 4, 5 and Notes
6 are exhaustive events.
(ii) In case of tossing a coin, the set of two outcomes, i.e., H and T are exhaustive
events.
(iii) In case of tossing of two dice, the set of possible outcomes are 6 × 6 = 36
which are given below:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

(4) Equally-Likely Events
The events are said to be equally-likely if the chance of happening of each event is equal or
same. In other words, events are said to be equally likely when one does not occur more often
than the others.
Examples: (i) If a fair coin is tossed, the events H and T are equally-likely events.
(ii) If a die is rolled, any face is as likely to come up as any other face. Hence, the
six outcomes -1 or 2 or 3 or 4 or 5 or 6 appearing up are equally likely
events.
(5) Mutually Exclusive Events
Two events are said to be mutually exclusive when they cannot happen simultaneously in a
single trial. In other words, two events are said to be mutually exclusive when the happening
of one excludes the happening of the other in a single trial.
Examples: (i) In tossing a coin, the events Head and Tail are mutually exclusive because
both cannot happen simultaneously in a single trial. Either head occurs or
tail occurs. Both cannot occur simultaneously. The happening of head
excludes the possibility of happening of tail.
(ii) In tossing a die, the events 1, 2, 3, 4, 5 and 6 are mutually exclusive because
all the six events cannot happen simultaneously in a single trial. If number
1 turns up, all the other five (i.e., 2, 3, 4, 5, or 6) cannot turn up.
(6) Complementary Events
Let there be two events A and B. A is called the complementary event of B and B is called the
complementary event of A if A and B are mutually exclusive and exhaustive.
Examples: (i) In tossing a coin, occurrence of head (H) and tail (T) are complementary
events.
(ii) In tossing a die, occurrence of an even number (2, 4, 6) and odd number (1,
3, 5) are complementary events.
(7) Simple and Compound Events
In case of simple events, we consider the probability of happening or not happening of single
events.
Example: If a die is rolled once and A be the event that face number 5 is turned up, then A is
called a simple event
In case of compound events, we consider the joint occurrences of two or more
events.

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