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Introduction

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☼ Probability    :   In a random experiment, let S be the sample space and E be the event. Then, E \subseteq S.  Then, we define  (if  m  =  n(E)  and  n =  n(S)) :

P(E)  =  \frac{\textup{Number of favourable cases to E}}{\textup{Number of possible outcome}s}  =  \frac{n(\textup{E})}{n(\textup{S})}  = \frac{m}{n}

Some Results on Probability  ( For events  A  and  B  )  :

(i) P (A) \leq 1,  P ( \emptyset )  =  0  and  P (S)  =  1,  where  A \subset S.

(ii) P (A \cup B)  =  P (A)  +  P (B)  –  P (A \cap B)

  \large \mapsto  If  A  and  B are mutually exclusive, then  A  B  =    and  in this case,

P (A \cup B)  =  P (A) + P (B).

(iii) P (A’ )   =    P \left (\overline{\textup{A}} \right )    =    P \left (a^{c} \right )    =    1  –  P (A).

(v) E and  F  are independent  \large \Leftrightarrow P (A \cap B)  =  P (A) · P (B).

 

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