NECO 2023 · Paper 1 · Q56

A box contains 20 oranges, 14 of them ripe and 6 unripe. If two oranges are taken one after the other with replacement, find the probability that one is ripe and the other unripe.

Worked solution (try it first)
  1. With replacement, each draw is ripe with probability 1420\frac{14}{20} and unripe with probability 620\frac{6}{20}.
  2. Ripe then unripe: 1420×620=84400\frac{14}{20} \times \frac{6}{20} = \frac{84}{400}, and unripe then ripe is the same.
  3. Add the two orders: 168400=2150\frac{168}{400} = \frac{21}{50}, option C.

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