In this lesson:
By the end of this lesson, you should be able to:
Today the overlap is exactly what we must handle carefully.
Draw one card from a standard 52-card deck.
How many cards are a king or a heart?
Try to count them before the next slide. Trust your first instinct — we're going to test it.
The obvious move:
This feels right — but let's actually list the cards and check.
The kings: K K K K — and the hearts include K.
The overlap was counted twice, so subtract it once:
The overlap holds the King of Hearts — it belongs to "king or heart," but only once.
Two events: = "face card", = "spade".
If you add , which card gets counted twice?
Name the card that lives in both events before advancing.
You just saw it: adding double-counts the shared outcomes.
The rule simply removes that double-count once.
Now we write the move you already understand as a formula.
For any two events and :
for one draw:
Add the two events
Subtract the overlap (the King of Hearts)
We listed 16 distinct cards that are a king or a heart.
The rule and the by-hand count agree — that's the rule working.
In every case, the term you subtract is :
Find the overlap first — that's the only new work the rule asks of you.
Everyday "or" can mean one or the other, not both. In probability, it doesn't.
Given , , .
Find — then check that your answer is between 0 and 1.
Apply the rule on your own, then sanity-check the result.
Always adding: forgetting to subtract the overlap Check for shared outcomes; ignoring them can push a probability above 1.
Exclusive "or": dropping the overlap instead of keeping it once A or B includes both — keep the overlap once, not zero times.
✓ ✓ Subtract because adding double-counts the overlap ✓ "Or" is inclusive — keep the overlap once, not zero
Next: disjoint events make the overlap zero — plus table "or" queries.
Click to begin the narrated lesson
Apply the Addition Rule