What are the odds in favor of rolling double sixes on a single roll of a fair pair of dice?

1/6

Step-by-step explanation:

There are six possible numbers that can be rolled twice.

1/6 x 1/6 = 1/36

by the rule of the product.

Since this can happen for 2,3,4,5,6, as well as for 1,

the probability of rolling the same number twice is

6⋅1/6⋅1/6=1/6