Home page for accesible maths 1 Probability (review)1.1 The Axioms of Probability 1.3 Independent Events

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1.2 Laws of Probability

An immediate consequence of the axioms of probability are the following results:

Partition Law: If $\{A_{1},\ldots,A_{m}\}$ form a partition of $A\subset\Omega$ , i.e. $A=\cup_{i=1}^{m}A_{i}$ and $A_{i}\cap A_{j}=\emptyset$ for all $i\neq j$ , then directly from Axiom 3:

\displaystyle\operatorname{\mathsf{P}}\left({A}\right)=\sum_{i=1}^{m}% \operatorname{\mathsf{P}}\left({A_{i}}\right).

Addition Law: For any events $A$ and $B$ then

\displaystyle\operatorname{\mathsf{P}}\left({A\cup B}\right)=\operatorname{% \mathsf{P}}\left({A}\right)+\operatorname{\mathsf{P}}\left({B}\right)-{\color[% rgb]{0.76,0.01,0}\operatorname{\mathsf{P}}\left({A\cap B}\right).}