The probability of rolling doubles on a single turn is the number of favorable cases over the number of total cases, the favorable cases are those when you get a double, the number of total cases is the number of total possible outcomes.
Now, the number of total possible outcomes is
[tex]6\times6=36.[/tex]The number of favorable cases is
[tex]6.[/tex]Therefore, the probability of rolling doubles is:
[tex]\frac{6}{36}=\frac{1}{6}\text{.}[/tex]Now, the probability of rolling double 3 times in succession is the product of rolling a double in a single turn, therefore:
[tex]P=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{216}.[/tex]Answer:
The probability of rolling doubles on a single turn is:
[tex]\frac{1}{6}\text{.}[/tex]The probability of rolling doubles 3 times in succession is:
[tex]\frac{1}{216}\text{.}[/tex]