Find the area of the region bounded by the $$x$$-axis and the curves defined by $$$y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}$$$

Three identical dice are rolled. The probability that the same number will appear on each of them is

A box contains $$24$$ identical balls of which $$12$$ are white and $$12$$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $$4$$th time on the $$7$$th draw is

If $$M$$ and $$N$$ are any two events, the probability that exactly one of them occurs is