Limes	Apples
Good	10	8
Bad	6	6

(a) 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 \(\log_{3} (4x + 1) - \log_{3} (3x - 5) = 2\).