A fruits basket contains 8 apples, 5 oranges and 2 mangoes. Half of the apples and 3 of the oranges are good and the rest are rotten. David randomly selects two fruits without replacement. By expressing your answers in four decimal places, find the probability that the two fruits selected are (i) (A) of different types, (В) apples if both fruits selected were rotten. (ii) State whether the events "good" and “rotten" fruits are mutually exclusive. Provide a reason for your answer.

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