Problem related to unbiased cubic dice Consider an unbiased cubic dice with opposite faces coloured identically and each face colour red, blue or green, such that each colour appears only 2 times on the dice.
If the dice is thrown thrice, what is the probability of obtaining red color on top face of the dice at least twice?
 A: Unbiased $\implies$ each face has equal chance of being on top.
Two faces each for the three colours $\implies$ equal chance of each colour.
So the probability of showing red on any one throw is just $r=\frac 13$, and the probability of not showing red is $q=(1-\frac 13) = \frac 23$
One way to view three throws is as a polynomial in the probailities:
$$(r+q)^3 = r^3 + 3r^2q + 3rq^2 + q^3$$
We want to know $p$, the chance of $2$ or $3$ reds, which is the first two terms there (with two or three factors of $r$):
\begin{align}
 p &=r^3 + 3r^2q = \left(\frac 13\right)^3+ 3\left(\frac 13\right)^2\cdot \frac 23 \\
&=\frac{1+3\cdot 1 \cdot 2}{3^3} = \frac{7}{27}\\
\end{align}

Edit: Doug M suggsts just laying out the possibilities and counting, which is a good check for a simple case...
$$\newcommand{RSq}{\color{red}{\blacksquare}}
 \newcommand{BSq}{\color{green}{\blacksquare}}
 \newcommand{GSq}{\color{blue}{\blacksquare}}
\begin{array}{cc}
1 & \RSq & \RSq & \RSq & \checkmark \\
2 & \RSq & \RSq & \BSq & \checkmark \\
3 & \RSq & \RSq & \GSq & \checkmark \\
4 & \RSq & \BSq & \RSq & \checkmark \\
5 & \RSq & \BSq & \BSq & \\
6 & \RSq & \BSq & \GSq & \\
7 & \RSq & \GSq & \RSq & \checkmark \\
8 & \RSq & \GSq & \BSq & \\
9 & \RSq & \GSq & \GSq & \\
10 & \BSq & \RSq & \RSq & \checkmark \\
11 & \BSq & \RSq & \BSq & \\
12 & \BSq & \RSq & \GSq & \\
13 & \BSq & \BSq & \RSq & \\
14 & \BSq & \BSq & \BSq & \\
15 & \BSq & \BSq & \GSq & \\
16 & \BSq & \GSq & \RSq & \\
17 & \BSq & \GSq & \BSq & \\
18 & \BSq & \GSq & \GSq & \\
19 & \GSq & \RSq & \RSq & \checkmark \\
20 & \GSq & \RSq & \BSq & \\
21 & \GSq & \RSq & \GSq & \\
22 & \GSq & \BSq & \RSq & \\
23 & \GSq & \BSq & \BSq & \\
24 & \GSq & \BSq & \GSq & \\
25 & \GSq & \GSq & \RSq & \\
26 & \GSq & \GSq & \BSq & \\
27 & \GSq & \GSq & \GSq & \\
\end{array}
$$
