Question

Suppose you have two disks each with 128 pie-shaped sectors. One disk has 32 red sectors and 96 white sectors. The other disk has 64 white sectors and 64 red sectors. The two patterns can be completely arbitrary. Can we place one over the other such that at least 64 sectors on each disk have the same color? Justify your answer using probabilistic methods and be sure to provide a sample space to support your reasoning.

Answer 1