07:41
@Nobodyrecognizeable The problem regarding probability is straightforward. A drawing of the coordinate axes(2D plane) is quite helpful. The first such step has probability $1$. The second such step has probability $\frac{3}{4}$ since retracing the step would not take us beyond the circle in $3$ steps. The third step is a bit more tedious to calculate, but after taking each possibility into account, the probability of the desired step is
$4\times \frac{3}{4}\times\frac1{16}+8\times\frac1{2}\times\frac1{16}=\frac{7}{12}$. Now, multiplying the probabilities of each step gives us $\frac{7}{16}=0.4375$, which is the desired answer
@N.Maneesh for the question 2.3 you referred, you are right for parts a and b. But, since $f$, $g$ are defined on $\mathbb{R}$, and since $g$ cannot be extended to a continuous function on a subset of reals of positive measure owing to the definition( the function has two different values on sets of nonzero measure), therefore, it is false
