p=∑P(AB)=∑P(4)P(B) ∑C070.3-×C0603=0 例1.16某实验室在器皿中繁殖成k个细菌的概率为 k=0,1,2,…,元>0 设所繁殖的每个细菌变为甲类菌或乙类菌的概率相等, 求所繁殖的细菌有i个成为甲类菌的概率。 解:B={繁殖的细菌中有i个成为甲类菌} A={繁殖了k个细菌} P(AK= ,k=0,1,2 P(B|4)=C(/2)(-1/2),i≤k,\C?i>k ,i≤k 所求概率为 P(B)=∑P(A)P(B|A)=∑PA)P(B|4) k!1 k!!(k-i) l=k-j o-d l2(k-)!2 =0 2 2() 0,1,2,( ) ( ) ( ) 3 0 3 0 k k k k k k p ∑ P A B ∑ P A P B = = = = 0.7 0.3 0.6 0.3 0.321 3 3 3 3 0 = 3 × = − − ∑ = k k k k k k k C C 例 1.16 某实验室在器皿中繁殖成 k 个细菌的概率为 , 0,1,2, , 0. ! = = > − λ λ e λ k " k P k k 设所繁殖的每个细菌变为甲类菌或乙类菌的概率相等， 求所繁殖的细菌有i 个成为甲类菌的概率。 解： B = {繁殖的细菌中有i 个成为甲类菌}； ={繁殖了k 个细菌} Ak , 0,1,2," ! ( ) = = − e k k P A k k λ λ ⎪⎩ ⎪ ⎨ ⎧ > ≤ = ⎩ ⎨ ⎧ > − ≤ = − i k C i k i k C i k P B A k i k i i k i k k 0, , 2 1 0 , ; (1/ 2) (1 1/ 2) , ; ( | ) 所求概率为： ( ) ( ) ( | ) = 0 k k P B ∑P Ak P B A ∞ = = ( ) ( | ) k k i ∑P Ak P B A ∞ = = k i k k i k e C k 2 1 ! λ −λ ∞ = ∑ = k k i k i k i k k e 2 1 !( )! ! ! ⋅ − ∑ ⋅ ∞ = −λ λ = l k i k i k i i i k i e = − − ∞ = − = − ∑ ) 2 ( ( )! 1 ) 2 ( ! λ λ λ l l i i l e ) 2 ( ! 1 ) 2 ( ! 0 λ λ λ ∑ ∞ = − = 2 ) 2 ( ! λ λ λ e i e i − = 2 ! ) 2 ( λ λ − e i i ，i = 0,1,2