Introduction to Statistics/Still confused?
Consider a simpler situation involving a deck of two cards: the queen of spades and the two of spades. We'll define our joint probability again as "the chance of drawing a queen or a spade", and naively express it as.
We can draw a card from our two card deck. We are guaranteed to draw a spade, so . Our chance of drawing a queen is 1 in 2, or . Let's add everything together. or 150%. This obviously doesn't make sense.
If we use the correct definition of the probability for this event:
we get the answer we expect.