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Consider a scenario of tossing a coin.

Either we get a head, or a tail is equally likely to appear. In other words, we can say the probabilities of both events are equal.

That is, P(getting a head) $$= \frac{1}{2}$$

P(getting a tail) $$= \frac{1}{2}$$

Similarly, let us consider another example of throwing a dice.

A dice has six faces, and their possible outcomes are $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$. On throwing a dice, we may end up in any one of the six faces. That is, on throwing a dice, the equally likely events are $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$.

In this chapter, we shall learn how to solve the problems when they are equally likely.

Important!
The empirical or experimental probability $$P(E)$$ of an event $$E$$ is defined as:

$$P(E) = \frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}$$

The theoretical probability or classical probability of an event $$E$$ is defined as:

$$P(E) = \frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$$

Note that $$0 \leq P(E) \leq 1$$