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Plain English Definition:
"A OR B" means: event A happens, event B happens, or BOTH happen. You "win" if at least one of the events occurs.
Example:
"Even OR Greater than 4" means the roll satisfies at least one condition:
Why can't we just add P(A) + P(B)?
If some outcomes satisfy BOTH conditions, they get counted twice when we add!
See the problem:
Even: 2, 4, 6
3 outcomes
> 4: 5, 6
2 outcomes
If we add 3 + 2 = 5, we're counting 6 twice (once as even, once as >4). But 6 is still just ONE outcome!
The Solution: Subtract the overlap
Add both, then subtract what we double-counted (the intersection).
What is the probability of rolling an even number OR a number greater than 4?
3 outcomes:
2 outcomes:
Only 6 satisfies BOTH:
This is what we'll subtract to fix the double-count.
Add the individual probabilities
This counts everything, but 6 is in both groups:
Subtract the overlap (6 was counted twice)
Remove one copy of the double-counted 6:
Final Answer:
List all outcomes that satisfy "even OR greater than 4":
Same answer! The formula works.