A survey of 240 people is recorded in a two-way table. Under 30: Yes 84, No 36. Aged 30 or above: Yes 56, No 64. Of the people who answered Yes, what fraction are under 30?

Work inside the Yes group only: 84 + 56 = 140 people answered Yes and 84 of them are under 30, so the fraction is 84/140 = 3/5. Dividing by the 240 surveyed gives 84/240 = 7/20, which uses the wrong base, and dividing by the 120 people under 30 gives 84/120 = 7/10 — that answers the reversed question, what fraction of the under-30s said Yes. The remaining 2/5 of the Yes group are aged 30 or above.