Probability of rolling three dice without getting a 6 in 8 rolls

Question

I know the propability of rolling three dice without getting a $6$ in $1$ roll is $91/216$, but what about rolling it in $8$ rolls consecutively with three dices?

Answer 1

The probability of rolling one die and not getting a $6$ is $\frac56$, so the probability of rolling three dice without getting a $6$ is $\left(\frac56\right)^3=\frac{125}{216}$, not $\frac{91}{216}$.

$\frac{91}{216}=1-\frac{125}{216}$ is therefore the probability of getting at least one $6$ when rolling three dice.

The probability of getting no sixes when you roll three dice $8$ times is the same as the probability of getting no sixes when you roll $3\cdot8=24$ dice, which is $\left(\frac56\right)^{24}$; this is about $0.01258$.