Question

設(shè)甲、乙、丙三人每次射擊命中目標的概率分別為0.7、0.6和0.5.

(1)三人各向目標射擊一次,求至少有一人命中目標的概率;

(2)三人各向目標射擊一次,求恰有兩人命中目標的概率;

(3)若甲單獨向目標射擊三次,求他恰好命中兩次的概率.

Answer 1

解:設(shè)A_k表示“第k人命中目標”，k=1,2,3.?

這里,A₁,A₂,A₃相互獨立,且P(A₁)=0.7,P(A₂)=0.6,P(A₃)=0.5,                                       ?

(1)至少有一人命中目標的概率為?

1-P(··)=1-P()P()P()=1-0.3×0.4×0.5=0.94.                    ?

(2)恰有兩人命中目標的概率為?

P(A₁·A₂·+A₁··A₃+·A₂·A₃)?

=P(A₁)P(A₂)P()+P(A₁)P()P(A₃)+P()P(A₂)P(A₃)                                         ?

=0.7×0.6×0.5+0.7×0.4×0.5+0.3×0.6×0.5=0.44.?

(3)所求概率為P₃(2)=C²₃(0.7)²(0.3)=0.441.