Question

Two cubical dice are thrown and their scores addes together if X= add is the sum of the scores on the two dice what is P(X is divided by 4)

Answer 1

When rolling two dice, there are $6^2=36$ outcomes for scores

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 1+1 & 1+2 & 1+3 & 1+4 & 1+5 & 1+6 \\ \hdashline 2 & 2+1 & 2+2 & 2+3 & 2+4 & 2+5 & 2+6 \\ \hdashline 3 & 3+1 & 3+2 & 3+3 & 3+4 & 3+5 & 3+6 \\ \hdashline 4 & 4+1 & 4+2 & 4+3 & 4+4 & 4+5 & 4+6 \\ \hdashline 5 & 5+1 & 5+2 & 5+3 & 5+4 & 5+5 & 5+6 \\ \hdashline 6 & 6+1 & 6+2 & 6+3 & 6+4 & 6+5 & 6+6 \\ \hdashline \end{array}$$

$$1+3=2+2=3+1=4$$

$$2+6=3+5=4+4=5+3=6+2=8$$

$$6+6=12$$

Let $X=$ is the sum of the scores on the two dice

$$P(X \text{is divided by 4})=\dfrac{9}{36}=\dfrac{1}{4}$$