Answer
$\frac{1}{9}$
Work Step by Step
For the tortoise to move ahead of the hare, the number on the second die
need to be larger than that of the first die.
There are three cases (12,13,23).
Case 1: $p=\frac{1}{6}\times\frac{2}{6}=\frac{1}{18}$
Case 2: $p=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$
Case 3: $p=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$
The total probability is the sum of all cases which gives $\frac{1}{9}$
