Question

In a throw of a pair of dice, what is the probability of getting a doublet?

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{5}{12}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$\frac{1}{6}$

There are six ways to roll 2 dice such that both dice have the same value

These are the outcomes $(1,1),(2,2),(3,3),(4,4,)(5,5)$ and $(6,6).$

To find the total number of outcomes, note that there are $6$ choices for the first die (values 1–6) and there are $6$ choices for the second die (again values 1–6) and so by the Multiplication Principle (MP) there are $36$ total outcomes from rolling two dice once.

Now we have the following:

P(getting a doublet) $=\frac{\text{Number of ways to get double}}{\text{Total number of outcomes}}$ $=\frac{6}{36}$$=\frac{1}{6}$

Thus, the probability of getting a doublet is $\frac{1}{6}$.