(a) Limes Apples Good 10 8 Bad 6 6 The table shows the number of limes and apples of the same size in a bag. If two of the fruits are picked at random, one ...

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(a) 

  Limes Apples
Good 10 8
Bad 6 6

The table shows the number of limes and apples of the same size in a bag. If two of the fruits are picked at random, one at a time, without replacement, find the probability that : (i) both are good limes ; (ii) both are bad fruits ; (iii) one is a good apple and the other a bad lime.

(b) Solve the equation \(\log_{3} (4x + 1) - \log_{3} (3x - 5) = 2\).