Question

What is the probability of getting a sum of 11 when a pair of dice is rolled?

• A. 0
• B. $\frac{1}{18}$
• C. $\frac{1}{12}$
• D. $\frac{1}{11}$

Answer 1

The correct option is B

$\frac{1}{18}$

Sample space for rolling a pair of dice
= S { (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) }

$\Rightarrow$ Total number of outcomes = 36

From the sample space, it is clear that the sum is 11, when there is a (5,6) and (6,5)

So, a sum of 11 happens in two cases.

Hence, the probability is $\frac{2}{36}$ = $\frac{1}{18}$