Let a sample space S consist of binary sequences as indicated: S = {100, 010, 001, 111}. A sequence is selected at random. The following events are defined: A - the first digit in the sequence is 1. B...

Let a sample space S consist of binary sequences as indicated:

S = {100, 010, 001, 111}. A sequence is selected at random.

The following events are defined:

A - the first digit in the sequence is 1.

B - the second digit in the sequence is 1.

C - the third digit in the sequence is 1.

Show that A, B, and C are pairwise independent but not mutually

independent.