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Complementary, sure and impossible events sheet
3-mark answer frame

Of 400 milk packets in a dairy van, 16 have leaked. One packet is picked at random. Find the probability that (i) it has leaked, (ii) it has not leaked. Explain why your two answers add up to 1.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Total packets = 400, leaked = 16. To find: P(leaked) and P(not leaked).
  2. 2 · Write the formula. P(E) = favourable outcomes ÷ total outcomes, and P(not E) = 1 − P(E).
  3. 3 · Find P(leaked). P(leaked) = 16/400 = 1/25.
  4. 4 · Use the complement. P(not leaked) = 1 − 1/25 = 24/25. Check: 400 − 16 = 384 good packets, and 384/400 = 24/25.
  5. 5 · Explain why they add to 1. 'Leaked' and 'not leaked' are complementary events. Every packet is one or the other, so 1/25 + 24/25 = 1.
  6. 6 · Check and box the answer. Box: P(leaked) = 1/25, P(not leaked) = 24/25.

Scoring tip: Name the complementary events in words. The reason is often a separate mark.