[3] A 6’ x 6’ x 6’ cube of packaged parts (1 cubic foot per part) were delivered to the Ballistic Research Laboratory. The packaged cube was unpacked, and parts were extracted in a prescribed order. Visual inspection, of the parts found deficiencies in 30 of the 216 parts delivered, making those parts bad. Someone observed that they would not have expected that many bad parts based on appearances of the exterior of the cube. That got individuals thinking. What if the supplier knew they were passing bad parts and attempted to bury most of the bad ones in the center 4’ x 4’ x 4’ cube hidden from view. To test this assumption, workers used the unpacking sequence to determine which parts were part of the exterior of the cube and which were in the interior. They also identified bad part positions and determined that half, 15, of the bad parts were in the center 4’ x 4’ x 4’ cube. Consider arrangements of the bad parts. What is the chance that placement at random would lead to what was observed? That is, If we were randomly selecting 30 positions in the 6’ x 6’ x 6’ to place bad parts, 

[a] What is the probability that exactly 15 of those positions selected came from the center cube? Use software to compute this. 

[b] What is the probability that 15 or more of those positions selected came from the center cube? Use software to compute this.