Complement rule
The chance that something happens at least once equals 1 minus the chance that it never happens. For independent tries, 'never' is the single 'no' chance multiplied by itself for each try.
In plain English
It's the quickest way to answer 'what are the odds something goes wrong?'. If each of 10 independent steps works 90% of the time, all ten work 0.9 to the power 10, about 35%, so at least one fails about 65% of the time. Small risks with many chances add up much faster than intuition suggests, which is most of what Murphy's law is.
Uncle Gary explains
If each person is late 10% of the time, a 20-person meeting starts on time only 12% of the time: 0.9 to the power 20.
Why it matters for your money
Twenty positions, each with a small chance of a nasty surprise this year, will very probably include at least one. Plan for some surprise.
Where we tested it
Related terms
All glossary terms. Educational content, not financial advice.