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

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

The points with position vectors $$a+b,$$ $$a-b,$$ and $$a+kb$$ are collinear for all real values of $$k.$$