If $$z=xy$$ $$ln(xy),$$ then

The maximum value of the function $$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$ (where $$x > - 1$$ ) occurs at $$x=$$________.

A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ________.

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is