Distributions of probabilities help to model our world, allowing us to estimate the likelihood of a said event or to approximate the variability of incidence. It is a common way of describing the probability of an event as well as possibly forecasting it, and the further calculation can be defined as follows:
The possibility of rolling a six on a 6-sided die is [tex]\frac{1}{6}[/tex]. There are
Three 6's are therefore [tex]\binom{1}{6}^3[/tex] likely to roll.
The probability that you don't roll a 6 is [tex]\binom{5}{6}[/tex] and you are not 6 double the record is[tex]\binom{5}{6}^2[/tex].
In 5 tests, there are 10 different ways [tex]\binom{5}{3}=10[/tex] to rolle three 6s.
Then we all have together:
[tex]\to 10 \times \binom{1}{6}^3 \times \binom{5}{6}^2 \approx 0.0322[/tex]
Therefore, the final answer is "0.0322".
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