Question

Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of dice is $8?$

Answer 1

Finding the probability that the sum of the two numbers appearing on the top of dice is $8$

Let $\text{P}\left(\text{E}\right)$ be the probability that the sum of the two numbers appearing on the top of dice is $8$

All possible outcomes when two dice are thrown at the same time$=$$$\begin{gathered} (1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) \end{gathered}$$

$\therefore$Number of possible outcomes$=36$

Outcomes with sum of the two numbers appearing on the top of dice is $8$$=(2,6),(3,5),(4,4),(5,3),(6,2)$

$\therefore$Number of favourable outcomes$=5$

We know that $\text{P}\left(\text{E}\right)\text{=}\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$

So, $\text{P}\left(\text{E}\right)$$=\frac{5}{36}$

Hence, probability that the sum of the two numbers appearing on the top of dice is $8$$=\frac{\mathbf{5}}{\mathbf{36}}$