Probability basics (Wahrscheinlichkeit)
Probability is a number between 0 and 1 (or 0-100%) that expresses how likely an event is. A probability of 0 means impossible, 1 means certain, and values between describe the frequency of an event across many repetitions — a fair coin lands heads 50% of flips on average, even though any single flip is heads or tails.
Why it matters
Insurance premiums, investment risk ratings, and loan default rates are all probabilities dressed up as products — an insurer prices a policy on the chance a claim occurs, not on certainty. Investment risk is routinely described as a probability of loss over a given horizon, and scam pitches ("guaranteed 20% monthly return") work precisely because they hide or misstate the odds behind the promise. Every money decision — taking a job, buying a policy, choosing an investment — is a bet on an uncertain outcome, whether or not anyone states the odds out loud. Reading probability correctly turns an implicit bet into an explicit, comparable one.
Worked examples
1. A 1-in-200 chance, read correctly. A specific risk — say, a defect that triggers a €20,000 repair — has a 1-in-200 (0.5%) chance of occurring in any single year. Over one year, 0.5% is genuinely small: roughly 1 case in 200 experiences it, and 199 don't. Over 20 years, the risk compounds, because each year is a fresh independent draw: the chance of at least one occurrence across those 20 years rises to 1 - 0.995^20 ≈ 9.5% — almost 1 in 10, far from "basically never." A small per-year probability and the cumulative probability over many years are not the same number; treating a long horizon as if it carries the one-year figure understates the real exposure.
2. Independent risks don't add up. Two unrelated risks — say, an appliance failure and, separately, a data breach — each carry an independent 10% chance of occurring this year. The chance that at least one of them occurs is not 10% + 10% = 20%; that double-counts the case where both happen. The correct calculation multiplies the chances of neither occurring, then subtracts from 1: 1 - (0.9 x 0.9) = 1 - 0.81 = 0.19, or 19%. Adding independent probabilities directly always overstates the combined risk, and the gap between the naive 20% and the correct 19% grows fast once more than two risks are stacked together.
Check yourself
Two independent risks each have a 10% chance of occurring this year. What is the probability (in %) that at least one of them occurs? Round to the nearest whole percent.
A specific risk has a 0.5% (1-in-200) chance of occurring in any single year. Over a 20-year period, is the probability of it occurring at least once still 0.5%?
Which of the following are values a probability can actually take? Select all that apply.
Convert a 1-in-200 chance into a percentage.