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

In a certain city only two newspapers $$A$$ and $$B$$ are published, it is known that $$25$$% of the city population reads $$A$$ and $$20$$% reads $$B$$ while $$8$$% reads both $$A$$ and $$B$$. It is also known that $$30$$% of those who read $$A$$ but not $$B$$ look into advertisements and $$40$$% of those who read $$B$$ but not $$A$$ look into advertisements while $$50$$% of those who read both $$A$$ and $$B$$ look into advertisements. What is the percentage of the population that reads an advertisement?

$$A, B, C$$ and $$D,$$ are four points in a plane with position vectors $$a, b, c$$ and $$d$$ respectively such that $$$\left( {\overrightarrow a - \overrightarrow d } \right)\left( {\overrightarrow b - \overrightarrow c } \right) = \left( {\overrightarrow b - \overrightarrow d } \right)\left( {\overrightarrow c - \overrightarrow a } \right) = 0$$$

The point $$D,$$ then, is the ................ of the triangle $$ABC.$$