Question

盒子中有7个球,4白3黑.从中任取3个球,求抽到白球数X的数学期望

概率论

Answer 1

4白3黑
X= 白球数
P(从中任取3个球, X=0) =C(4,3)/C(7,3) =4/35
P(从中任取3个球, X=1) =C(4,2).C(3,1)/C(7,3) =18/35
P(从中任取3个球, X=2) =C(4,1).C(3,2)/C(7,3) =12/35
P(从中任取3个球, X=3) =C(4,0).C(3,3)/C(7,3) =1/35
E(X)
=(0).P(从中任取3个球, X=0) +(1).P(从中任取3个球, X=1)+(2).P(从中任取3个球, X=2)
+(3).P(从中任取3个球, X=3)
=0 + 18/35 + 24/35 +3/35
=45/35
=9/7