Question

Make a table in which you list all possible outcomes of rolling two dice. Call the dice A and B. What is the probability of rolling

(a) a 7,

(b) any double, and

(c) a 6 or an 8?

You can give the probabilities as fractions, such as 3/36.

Short answer

Therefore, the probabilities are:

$$\begin{gathered} a)p=\frac{1}{6} \\ b)p=\frac{1}{6} \\ c)p=\frac{5}{18}\hspace{0.17em} \end{gathered}$$

Step-by-step solution

Given information

Two dice are rolled. Call the dice A and B.

Explanation

The table of all possible outcomes when two dice are rolled:

A	B	A	B
1	1	4	1
1	2	4	2
1	3	4	3
1	4	4	4
1	5	4	5
1	6	4	6
2	1	5	1
2	2	5	2
2	3	5	3
2	4	5	4
2	5	5	5
2	6	5	6
3	1	6	1
3	2	6	2
3	3	6	3
3	4	6	4
3	5	6	5
3	6	6	6

Explanation

There are a total of 6 dice combinations, with a result of 7. As a result, the probability is:

$$\begin{gathered} p=\frac{6}{36} \\ p=\frac{1}{6} \end{gathered}$$

Because there are 6 possible double combinations, the probability is

$$\begin{gathered} p=\frac{6}{36} \\ p=\frac{1}{6} \end{gathered}$$

There are five combinations in which 6 is possible, and five combinations in which 8 is plausible, hence a total of ten possibilities. As a result, probability is:

$$\begin{gathered} p=\frac{10}{36} \\ p=\frac{5}{18} \end{gathered}$$