Addition Rule

Addition Rule

If and are any two mutually exclusive events, then

Suppose I have two biased coins, coin $A$ and coin $B$. Coin $A$ flips heads with probability 0.6, and coin $B$ flips heads with probability 0.3. I flip both coins once. What's the probability I see two different faces?

Proof:
If and are events consisting of equally-likely outcomes, and furthermore and are mutually exclusive (meaning they have no overlap), then