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← Probability of Complementary Events
Rung 2 of 4 · The method

Actually Working One Out

One rule, one subtraction. Take the chance you know away from 1, and the complement falls out.

PractiseRead the question, hit "show me the steps" if you're stuck, then type the complement and check yourself. New question for a fresh one.
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There's really only one move: P(not A) = 1 − P(A). The whole is always 1, so peel the event off and what's left is its complement.

The One Rule

Take the chance you know away from 1. If you know the chance an event happens, the chance it doesn't is just 1 minus that. Written tidily: P(not A) = 1 − P(A). That's the whole method — there's no step two.

A Worked One

A spinner lands on brass with probability 3/8. What's the chance it doesn't? Write the rule, drop the number in, subtract: P(not brass) = 1 − 3/8 = 8/8 − 3/8 = 5/8. Notice the little trick — to subtract a fraction from 1, write 1 as 8/8 (the same denominator), then it's an easy take-away on the top.

Say it plainly: to subtract from 1, rewrite 1 with the matching denominator — 1 = 8/8 — then just subtract the numerators. 8/8 − 3/8 = 5/8.

Fractions, Decimals or Percentages

The rule works in any costume. As a decimal: 1 − 0.375 = 0.625. As a percentage: 100% − 37.5% = 62.5%. Same chance, three outfits — the toy accepts whichever you fancy, so pick the one that matches how the question was asked.

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Us, Thinking Out Loud

Could you teach me the rule — and the "write 1 as 8/8" trick — without looking?

When would you rather answer in percentages than fractions?