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Unit 12: Probability and Expected Value

4. Event: The occurrence or non-occurrence of a phenomenon is called an event. For example, Notes
in the toss of two coins, there are four exhaustive outcomes, viz. (H, H), (H, T), (T, H),
(T, T). The events associated with this experiment can be defined in a number of ways. For
example, (i) the event of occurrence of head on both the coins, (ii) the event of occurrence
of head on at least one of the two coins, (iii) the event of non-occurrence of head on the two
coins, etc.

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Caution An event can be simple or composite depending upon whether it corresponds to
a single outcome of the experiment or not. In the example, given above, the event defined
by (i) is simple, while those defined by (ii) and (iii) are composite events.

Example: Find the probability of obtaining an odd number in the roll of an unbiased die.
Solution:
The number of equally likely, mutually exclusive and exhaustive outcomes, i.e., n = 6. There are
three odd numbers out of the numbers 1, 2, 3, 4, 5 and 6. Therefore, m = 3.
Thus, probability of occurrence of an odd number

Example: What is the chance of drawing a face card in a draw from a pack of 52 well-
shuffled cards?
Solution:

Total possible outcomes n = 52.
Since the pack is well-shuffled, these outcomes are equally likely. Further, since only one card is
to be drawn, the outcomes are mutually exclusive.

There are 12 face cards, m = 12.
12 3
Thus, probability of drawing a face card = =
52 13

Task What is the probability that a leap year selected at random will contain 53 Mondays?

Self Assessment

State whether the following statements are true or false:

1. The concept of probability originated from the analysis of the games of chance in the
17th century.
2. The theory of probability is a study of Statistical or Random Experiments.

3. It is the backbone of Statistical Inference and Decision Theory that are essential tools of the
analysis of most of the modern business and economic problems.
4. A phenomenon or an experiment which can result into more than one possible outcome,
is called a random phenomenon or random experiment or statistical experiment.
5. The result of a toss can be a head or a tail. thus, it is a non random experiment

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