Understanding the D100 Dice Roller
Probability calculations quantify uncertainty — expressing how likely events are on a 0 to 1 scale. Building intuition for these numbers is one of the highest-value skills in decision-making under uncertainty.
Core rules
- Addition rule: P(A or B) = P(A) + P(B) − P(A and B). For mutually exclusive events, the last term is 0.
- Multiplication rule: P(A and B) = P(A) × P(B|A). For independent events, P(B|A) = P(B), simplifying to P(A) × P(B).
- Complement: P(not A) = 1 − P(A). Often easier to calculate the complement and subtract.
- Bayes' theorem: P(A|B) = P(B|A) × P(A) / P(B). Updates the probability of a hypothesis given new evidence.
Common intuition traps
- Gambler's fallacy: past independent outcomes don't affect future ones. A coin that's landed heads 10 times still has 50% probability on the next flip.
- Base rate neglect: rare events remain unlikely even after a positive test. A disease affecting 1 in 10,000 that produces a 99% accurate positive test: most positives are still false positives.
Frequently Asked Questions
How accurate are the results?
The D100 Dice Roller applies a standard formula to your inputs — accuracy depends on how precisely you measure those inputs. For planning and estimation, results are reliable. For high-stakes or professional decisions, cross-check the output with a domain expert or primary source.
What sample size do I need for reliable results?
It depends on the desired confidence level, margin of error, and population variance. For a typical survey (95% confidence, ±5% margin), n ≈ 385 for a large population. Smaller samples are fine for exploratory analysis, but don't over-interpret the results — widen your confidence intervals to reflect the uncertainty.