The probability of r successes in n trials is
[tex]C(n,r)p^r(1-p)^{n-r}[/tex] where C(n,r) is the number of combinations of n things taken r at a time...
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
Define "success" as getting a 6 on the die. Then the probability of success is [tex]p=\frac{1}{6} [/tex] and the probability of "failure" is [tex]1-p=\frac{5}{6} [/tex].
The probility is [tex]C(4,2)\left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^2=6\left(\frac{1}{36}\right) \left( \frac{25}{36}\right)=0.11574=11.6%[/tex]
