A cube, measuring four inches on a side, is painted. It is then cut into 64 one-inch cubes.?

Question

One of the smaller cubes is chosen at random and tossed. Find the probability that none of the five faces that are showing is painted.

Answer 1

of the 64s;

8 have 3 painted faces,

24 have 2 painted faces,

24 have 1 painted face,

8 have 0 painted face.

P(none of the five faces that are showing is painted)

= P(land ON the only painted face)*P(1 painted face chosen) + P(0 painted face chosen)

= (1/6)*(24/64) + 1*(8/64)

= 1/16 + 1/8

= 3/16