Probability of Event

Suppose a coin is tossed at random. You have two possible outcomes, Head (H) and Tail (T). We may assume that each outcome H or T is as likely to occur as the other. In other words, we say that the two outcomes H and T are equally likely.

Similarly, when you throw a die, it seems reasonable to assume that each of the six faces (or each of the outcomes 1, 2, 3, 4, 5, 6) is just as likely as any other to occur. In other words, the six outcomes 1, 2, 3, 4, 5 and 6 are equally likely.

Event

One or more outcomes constitute an event of an experiment. For example, in throwing a die an event could be "the die shows an even number". This event corresponds to three different outcomes 2, 4 or 6.

However, the term event also often used to describe a single outcome. In case of tossing a coin, "the coin shows up a head" or "the coin shows up a tail" each is an event, the first one corresponds to the outcome H and the other to the outcome T.

An event having only one outcome of the experiment is called an elementary event.

Probability of Event

The probability of an event E, written as P(E), is defined as:

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