AND multiplies, OR adds: the SAT probability mix-up
Two coins, both heads: if you added ½ + ½ = 1, you just proved certainty — and answered a real SAT distractor.
Why it happens
The words 'and'/'or' read as connectors, not operations. Without a rule anchored to them, addition is the default reflex.
See the trap
P(two fair coins both land heads)?
✗ The trap: ½ + ½ = 1.
✓ The fix: ½ × ½ = ¼.
How to actually fix it
- 'Both/and' → multiply (independent events).
- 'Either/or' (mutually exclusive) → add.
- Check the bound: probabilities above 1 mean you added when you should have multiplied.
Made this mistake on a real question?
Practice Problem-Solving and Data Analysis questions here. Miss one and it is logged with the exact error, then brought back until you beat it.
Practice Problem-Solving and Data Analysis →FAQ
What if the events overlap?
Then P(A or B) = P(A) + P(B) − P(A and B). The SAT tests the overlap subtraction with two-way tables.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.