Question

设甲、乙、丙三人每次射击命中目标的概率分别为0.7、0.6和0.5.

(1)三人各向目标射击一次,求至少有一人命中目标的概率;

(2)三人各向目标射击一次,求恰有两人命中目标的概率;

(3)若甲单独向目标射击三次,求他恰好命中两次的概率.

Answer 1

解:设A_k表示“第k人命中目标”，k=1,2,3.?

这里,A₁,A₂,A₃相互独立,且P(A₁)=0.7,P(A₂)=0.6,P(A₃)=0.5,                                       ?

(1)至少有一人命中目标的概率为?

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

(2)恰有两人命中目标的概率为?

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)所求概率为P₃(2)=C²₃(0.7)²(0.3)=0.441.