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JAMB 2012 · UTME · Q50

The probabilities that a man and his wife live to 80 years are 23\frac23 and 35\frac35 respectively. Find the probability that at least one of them will live to 80 years.

Worked solution (try it first)
  1. "At least one" is the complement of "neither".
  2. The chances of not living to 80 are 1−23=131 - \frac23 = \frac13 and 1−35=251 - \frac35 = \frac25.
  3. Neither lives to 80: 13×25=215\frac13 \times \frac25 = \frac{2}{15}.
  4. So at least one does: 1−215=13151 - \frac{2}{15} = \frac{13}{15}, option D.

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