Adding probabilities when you should multiply
"The AND/OR Mixup"
The Mistake in Action
A coin is flipped twice. Find the probability of getting two heads.
Wrong: $P(HH) = \frac{1}{2} + \frac{1}{2} = 1$
Why It Happens
Students confuse when to add and when to multiply. They may think "two events" means add, without considering whether it's AND or OR.
The Fix
AND = Multiply (both events must happen) OR = Add (either event can happen)
"Two heads" means Head AND Head: $$P(HH) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$$
Memory aid:
- "AND" makes it harder (probability gets smaller) → multiply
- "OR" gives more options (probability gets larger) → add
Check: Getting two heads should be less likely than getting one head!
Spot the Mistake
Can you identify where this student went wrong?
Find P(two heads) for two coin flips
$P(HH) = \frac{1}{2} + \frac{1}{2} = 1$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: