The formula
P(A) = favourable cases ÷ possible cases
What it means
This is Laplace's rule, and its only condition is that every case be equally likely. It works for dice, cards, draws and urns, and it does not work when the cases are not: the chance of rain tomorrow is not “one in two” because it either rains or it does not.
How to work it out by hand
- Count how many different outcomes there can be in total
- Count how many of them work for you
- Divide the favourable ones by the possible ones
- Multiply by a hundred if you want a percentage
What is worth knowing
There are three ways of stating the same probability and they are worth keeping apart. The percentage works for middling figures; “one in X” is the only one that lands when the probability is tiny, which is why lotteries are quoted that way; and betting odds, “one to five”, compare the favourable cases against the unfavourable ones rather than against the total. A die has a sixth of a chance, is “one in six” and pays “five to one”: three different numbers for the same event, and half the confusion around betting lives right there.