Explaining Odds to a Committee: Counting Before Estimating
Advisers are often asked how likely something is. The clearest answers come from counting the possible outcomes first, and a lottery is the cleanest worked example there is.
Start with what can be counted
Some probabilities can be worked out exactly, because every outcome is known and equally likely. The mathematics is that of combinations: how many ways a set of items can be chosen when order does not matter.
Why lotteries make good teaching material
A number-draw lottery has fixed rules and no judgement involved, so the chance of each prize can be derived step by step. Lottery mathematics is a standard classroom example for that reason.
A fully worked case
For anyone who wants to see every step written out, this Traditional Chinese page derives the jackpot odds of Taiwan's Super Lotto, roughly 1 in 22 million, and the odds of each of the ten prize tiers (威力彩機率). It shows where the denominator comes from and then counts the winning combinations tier by tier, which is exactly the method to demonstrate.
Moving to things that cannot be counted
Most real questions, such as whether a project will finish on time, have no fixed list of outcomes. There you estimate from past cases and say how confident you are. Being clear about which kind of number you are giving is half the job.
Presenting it
- Use frequencies. "About 1 in 20" is understood more reliably than "5 per cent".
- Give the comparison. A small chance means more next to a familiar one.
- Say what the number rests on: counted, measured or judged.
Entry reviewed 2026-10-13