Question

what is the theoretical probability a rolling a to round to three decimal places

Answer 1

For the experiment of rolling a fair dice, each face has an equal probability of showing up.

Let 'p' be the probability of getiing a particular face.

So the probability of rolling any of the 6 face is 'p'.

Now, the sum of all probability should be unity,

$\begin{gathered} P(1)+P(2)+P(3)+P(4)+P(5)+P(6)=1 \\ p+p+p+p+p+p=1 \\ 6p=1 \\ p=\frac{1}{6} \end{gathered}$

Thus, the probability of any face is 1/6.

Hence, it concludes that the theoritical probability of rolling a 2 is equal to 1/6.