2)A1,A2…An是两两互不相容的事件,则有 (A1∪A20…UAn)=P(A1)+P(A2)+…+P(A1) 证明:设A=,=n+1,n+2,…,则 ∪A,=(4)②U…U必U…=∪ n P(∪A1)=P(U P(A1)+P(A2)+…+P(An)+P() P(A1)+P(A2)+…+P(An) P(A1UA2∪.…UAn)=P(A1)+P(A2)+…+P(A2) A A 1 2 An , ,L 是两两互不相容的事件，则有 P A( ) A An n P A( ) P A( ) P A( ) 1 2 U ULU = + 1 2 +L+ 证明:设 A i n n i = ∅, , = + 1 2 + ,L，则 U U U U L U U L U ∞ = = = = ∅ ∅ = 1 1 1 ( ) , n n i n i An Ai Ai P An i P A n i n ( ) = ( ) = ∞ =1 1 U U = P A( )1 2 + P A( )+L L + P A( n ) + P(∅)+ = P A + P A + + P An ( ) ( ) ( ) 1 2 L ∴ P A( ) A An n P A( ) P A( ) P A( ) 1 2 U ULU = 1 + 2 +L+