Multiply for AND, add for OR
- The idea
- Predict
- See it
- Why
- Check
The idea
“Chances that must both happen get added, and chances where either one counts get multiplied.”
More offspring sounds like more chances, so adding feels natural. Needing every one of them to turn out a certain way is a higher bar, so the chance gets smaller.
The short version
The mistake: Chances that must both happen get added, and chances where either one counts get multiplied.
What's actually true: Multiply when independent events must all happen. Add when any one of several outcomes that can't happen together will do.
- The product rule is for AND. When independent events must all happen, multiply their chances. Independent means one doesn't change the other's chance.
- The sum rule is for OR. When any one of several outcomes will do, and no two can happen together, add their chances.
- In an Aa × Aa cross, a dominant-looking offspring is AA or Aa, so 1/4 + 1/2 = 3/4. Multiplying gives 1/8, rarer than AA alone, which can't be.
On the exam: AND makes a chance smaller, OR makes it bigger. If your answer went the wrong way, you swapped the rules.