Computing the probability (or percentage) of the event when the question asked for its opposite — or vice versa. The maths is perfect; it answers the mirror-image question.
Questions flip polarity in a single word: 'NOT defective', 'at least one', 'fails to'. Reading at speed, the eye catches the subject and misses the negation.
Underline (mentally or literally) the polarity words before computing: not, at least, fewer than, fails. For probability, decide explicitly whether you want P or 1−P before any arithmetic — and remember 'at least one' is usually 1 − P(none).
What is 30% of 1,680?
x% of y = (x ÷ 100) × y. The correct answer is 504.0. Traps to avoid: 168.0 comes from the "wrong percent" error; 5,040.0 comes from the "decimal slip" error; 560 comes from the "divided" error; 1,176.0 comes from the "complement" error.
This trap appears in 25 of our questions, across: Percentage of · Fraction–decimal–percent.
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