Probability is a measure of uncertainty. There are three different approaches to define the probability.

**Definitions
of Probability**

Probability is a measure of uncertainty. There are three
different approaches to define the probability.

If the sample space S, of an experiment is finite with all its
elements being equally likely, then the probability for the occurrence of any
event, A, of the experiment is defined as

The above definition of probability was used until the introduction
of the axiomatic method. Hence, it is also known as classical definition of
probability. Since this definition enables to calculate the probability even
without conducting the experiment but using the prior knowledge about the
experiment, it is also called as a priori probability.

What is the chance of getting a king in a draw from a pack of 52
cards?

In a pack there are 52 cards [n(s) = 52] which is shown in fig.
8.2

Let *A* be the event of
choosing a card which is a king

In which, number of king cards *n*(*A*) = 4

Therefore probability of drawing a card which is king is = P(A)

A bag contains 7 red, 12 blue and 4 green balls. What is the
probability that 3 balls drawn are all blue?

From
the fig. 8.3 we find that:

Total number of balls = 7+12+14=23 balls

Out of 23 balls 3 balls can be selected in =
n(s)= 23C_{3} ways

Let A be the event of choosing 3 balls which
is blue

Number of possible ways of drawing 3 out of 12
blue balls is = n(A)=12C_{3} ways

A class has 12 boys and 4 girls. Suppose 3 students are selected
at random from the class. Find the probability that all are boys.

From the fig 8.4, we find that:

Total number of students = 12+4=16

Three students can be selected out of 16 students in 16C_{3}
ways

If the random experiment is repeated n times under identical
conditions and the event A occurred in n(A) times, then the probability for the
occurrence of the event A can be defined (Von Mises) as

Since computation of probability under this approach is based on
the empirical evidences for the occurrence of the event, it is also knows as relative frequency or
a posteriori probability.

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11th Statistics : Chapter 8 : Elementary Probability Theory : Definitions of Probability |

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