Comprehensive Calculator Guide
This calculator gives, for three independent events, the chance of all three, none, at least one, exactly one and exactly two. Three stages at 0.9, 0.8 and 0.7 all succeed only 0.504 of the time, but at least one succeeds 0.994 of the time.
Chains and backups
All three = the product of the probabilities; none = the product of the complements; at least one = 1 − none. Stages in series are weaker than the weakest; backups in parallel are far stronger.
How to Use
- Enter the three probabilities.
- Make sure the events are independent.
- Press “Calculate” to see each outcome.
Formula Used
All = P(A)P(B)P(C) | None = (1 − P(A))(1 − P(B))(1 − P(C)) | At least one = 1 − None
Practical Examples
- Example 1
- 0.9, 0.8, 0.7: all 0.504, at least one 0.994.
- Example 2
- 0.95, 0.9, 0.85: at least one 0.99925.
Important Tips
- The four outcomes add to 1.
- Add an independent backup for reliability.
- Use conditional probability for dependent events.
Common Mistakes to Avoid
- Adding the three probabilities.
- Forgetting “exactly one” excludes the others.
- Assuming independence with a shared power source.
Frequently Asked Questions
- Exactly two?
- Add the three ways two can happen without the third.
- Why is “all” so small?
- Each extra condition multiplies by a number under 1.
- More than three events?
- The same rules apply.