Introduction to Statistics/Still confused?

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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.
P(Queen \cup \spadesuit) = P(Queen) + P(\spadesuit)
We can draw a card from our two card deck. We are guaranteed to draw a spade, so P(\spadesuit) = 1. Our chance of drawing a queen is 1 in 2, or \frac{1}{2}. Let's add everything together. P(Queen \cup \spadesuit) = 1.5 or 150%. This obviously doesn't make sense, unless you are a professional athlete.

If we use the correct definition of the probability for this event:
P(Queen \cup \spadesuit) = P(Queen) + P(\spadesuit) - P(Queen \cap \spadesuit)
= 0.5 + 1.0 − 0.5
we get the answer we expect.

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