没取到黑球的概率是(得0分)
P(0)=C(4)(4)/C(7)(4)
=1/35
取到1个黑球的概率是(得1分)
P(1)=C(4)(3)*C(3)(1)/C(7)(4)
=12/35
取到2个黑球的概率是(得2分)
P(2)=C(4)(2)*C(3)(2)/C(7)(4)
=18/35
取到3个黑球的概率是(得3分)
P(3)=C(4)(1)*C(3)(3)/C(7)(4)
=4/35
所以得分期望是
0*P(0)+1*P(1)+2*P(2)+3*P(3)
=0*1/35+1*12/35+2*18/35+3*4/35
=(12+36+12)/35
=60/35
=12/7