# Current Affairs JEE Main & Advanced

## Classical Definition of Probability

Category : JEE Main & Advanced

If a random experiment results in n mutually exclusive, equally likely and exhaustive outcomes, out of which m are favourable to the occurrence of an event A, then the probability of occurrence of A is given by

$P(A)=\frac{m}{n}=\frac{\text{Number of outcomes favourable to }A}{\text{Number of total outcomes}}$

It is obvious that $0\le m\le n$. If an event A is certain to happen, then $m=n,$ thus $P(A)=1$.

If A is impossible to happen, then $m=0$ and so $P(A)=0$. Hence we conclude that $0\le P(A)\le 1$.

Further, if $\bar{A}$ denotes negative of A i.e. event that A doesn’t happen, then for above cases m, n; we shall have

$P(\bar{A})=\frac{n-m}{n}=1-\frac{m}{n}=1-P(A)$ ,$\therefore$  $P(A)+P(\bar{A})=1$.

Notations : For two events A and B,

(i) $A'$ or $\bar{A}$ or ${{A}^{C}}$ stands for the non-occurrence or negation of A.

(ii) $A\cup B$ stands for the occurrence of at least one of A and B.

(iii) $A\cap B$ stands for the simultaneous occurrence of A and B.

(iv) $A'\cap B'$ stands for the non-occurrence of both A and B.

(v) $A\subseteq B$ stands for “the occurrence of A implies occurrence of B”.

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