Probability is a chance of prediction of happening of an event. While working with probability we must know about the some terms such as event, sample space, experiment, like events, complementary events and mutually exclusive events etc.

When something happens it is said that an event has occurred. All the events are always associated to some random experiment.

**For Example:** flipping a coin is an experiment and getting a head or tail are two events which are associated to this experiment.

In probability the complement of any event is the not of that event. In a random experiment, the outcome must occur on every trial and the probabilities of all possible events must total to one.

The probability of complement of an event must be unity minus the probability of the event. For example we have an event B, and then its complement is not B. It is denoted by B$^C$, B', or by a bar over B ($\bar{B}$).

When something happens it is said that an event has occurred. All the events are always associated to some random experiment.

In probability the complement of any event is the not of that event. In a random experiment, the outcome must occur on every trial and the probabilities of all possible events must total to one.

The probability of complement of an event must be unity minus the probability of the event. For example we have an event B, and then its complement is not B. It is denoted by B$^C$, B', or by a bar over B ($\bar{B}$).

The probability of event $B$ is given by $P (B)$ and the probability of its complement by $P (B’)$.

In general this is to remember that the total event of two complementary events is always equal to 1, that is,

$P (B) + P (B’)$ = 1

Thus the probability of complement of event B is given by P (B’) = 1 – P (B).

There are many examples of complementary events associated to different experiments. Some of them are given below:

So it can be clearly seen that we have endless number of options for complementary events. To find out the probability of an event also, sometimes we use the complement event probability for easier calculation.

P (getting a 5) = $\frac{1}{6}$.

Hence the probability of not getting a five is the complementary event of getting a 5. So the probability is given by:

P (not getting 5) = 1 – P (getting a 5) = 1 – $\frac{1}{6}$ = $\frac{5}{6}$.

Hence the probability of not getting a white ball = 1 – $\frac{1}{2}$ = $\frac{1}{2}$.

So, probability of getting a jack or king, P (jack or king) = $\frac{8}{52}$ = $\frac{2}{13}$

Hence the probability of not getting a jack or a king is given by:

P (not getting a king or a jack) = 1 – $\frac{2}{13}$ = $\frac{11}{13}$.