A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The probability that $$X\ge3$$ equals :

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

Let $$f$$ be a non-negative function defined on the interval $$[0,1]$$.

If $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}dt} = \int\limits_0^x {f(t)dt,0 \le x \le 1} } $$, and $$f(0) = 0$$, then