Question

explain classical approach to probability

Answer 1

If an event A occurs in m times out of a total of n exhaustive, mutually exclusive and equally likely experiments, then the probability of the occurrence of event A is m/n .

p(A) = m/n

The sample space corresponding to the experiment ‘tossing a fair coin' .
A1 = {H}, A2 = {T}



Sample space, Ω, for the experiment ‘tossing a fair coin'

In this case, the two possible events are getting heads and getting tails. These two events are collectively exhaustive because all the elements in the sample space, shown in the above Figure, are falling in either of the two possible events. They are mutually exclusive because there is no overlap in the sample space corresponding two the two possible events.

To apply this definition one must have prior knowledge on the sample space associated to the experiment and the sample space associated to the event. For example, what is the probability of getting a card of a particular color when one card is randomly picked from a pack of cards? Since the information on the color composition of cards is known (i.e. m and n are known to be 26 and 52 respectively), answer to this question is 0.5.

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