Question

two dice are rolled. what is the probability that the sum of the numbers rolled is either 8 or 10? express your answer as a fraction

Answer 1

Given,

The number of dice rolled is 2.

The total number of outcomes on rolling two dice is,

$6^2=6\times6=36$

The number of outcomes which have the suum 8 or 10 is,

$\begin{gathered} A=\mleft\lbrace(2,6\mright),\text{ (3,5), (4,4), (4,6), (5,3), (5,5), (6,2), (6,4)}\} \\ n(A)=8 \end{gathered}$

The probability that the sum of the numbers rolled is either 8 or 10 is,

$\begin{gathered} P(A)=\frac{n(A)}{S} \\ =\frac{8}{36} \\ =\frac{2}{9} \end{gathered}$

Hence, the probability is 2/9.