When 'at least one' wrecks your enumeration, flip the question — counting the failure case is almost always faster.
Method · Complement
Intro
When the event you want is hard to count directly — especially when it's an “at least one” condition — compute $1 - P(\text{not it})$ instead. The complement is almost always a single, easy-to-count outcome.
✓ Intro · expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine — being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
✓ Try first · expand
Worked example
A fair coin is flipped 3 times. What is the probability of getting at least one head?
✓ Worked example · expand
Practice 1 of 3Type a fraction, decimal, or expression — mathjs parses it.
✓ Practice · expand
Reflection
In your own words, when is flipping to the complement the right move? What's the cue in the problem statement that tips you off?