Measurement of Probability
Classical definition of probability or priori probability
Our treatment of probability theory will be restrictive in two respects. First, for the sake of simplicity, we shall assume that the total number of elementary events in the sample space is finite (say r). Thus, the treatment will not be applicable to cases where the number of elementary events is infinite.
Secondly, it will be assumed that the experiment is such that the r elementary events are equally likely- in the sense that, when all relevant evidence is taken into account, no one of them can be expected to occur in preference to the others.
The probability P(A) of any event A is then
P(A) = (r(A))/r
where r(A) is the number of elementary events favourable to A
The above equation, gives what is called the ‘Classical Definition of Probability’.
We shall use this definition to find out the probability of outcomes in the following cases:
1. Suppose, we toss a die. What is the probability of 4 coming up?
Since there are six mutually exclusive and equally likely outcomes, out of which 4 is only one, the probability of 4 coming up is 1/6.
2. Suppose we toss 2 coins. We can have the following outcomes: both heads HH; one head and one tail, TH or HT; and both tails, TT ( H= Head; T= Tail). Suppose, we want to know the probability of HH.
HH being one of the four equally likely outcomes, the probability of obtaining HH is ¼.
3. Suppose we throw 2 dice and we want the probability of a total of 7 points.
A total of 7 can come in 6 ways (1-6, 2-5, 3-4, 4-3, 5-2 or 6-1). So the numerator will be 6. Since we have 6 sides for each die, the total number of ‘equally likely’, ‘mutually exclusive’ outcomes is 6×6 = 36. So the chance of getting a total of 7 when we throw 2 dice is 6/36 (or 1/6).
