Solution: Solution: (1) Choose four points ABCD-a1b1c1d1from the eight vertices of the cube, and * * has.

C

four

eight

=70 cases, when there are four * * * faces, * * has 12 cases.

∴P(ξ=0)=

12

70

=

six

35

.

(2) When there is no * * plane at four points, the volume of tetrahedron has the following two situations:

① Four points are on the diagonal of the opposite and different planes, and the volume is 1-4×.

1

six

=

1

three

Go * * *, there are two ways;

② Three of the four points are on one side and the other is on the opposite side, and the volume is

1

six

There are 70- 12-2=56 ways to * *.

The ∴ξdistribution list is

ξ

1

three

1

six

P

six

35

1

35

28

35

Mathematical expectation E(ξ)= 1

1

three

×

1

35

+

1

six

×

28

35

=

1

seven

.