A coin is tossed twice. Consider the following events.

[math]A[/math]: Heads on the first toss.

[math]B[/math]: Heads on the second toss.

[math]C[/math]: The two tosses come out the same.

• Show that [math]A[/math], [math]B[/math], [math]C[/math] are pairwise independent but not independent.
• Show that [math]C[/math] is independent of [math]A[/math] and [math]B[/math] but not of [math]A \cap B[/math].