Question

Two fair dice are rolled. Then, the probability of getting a composite number as the sum of face values is equal to

• A. $\frac{7}{12}$
• B. $\frac{5}{12}$
• C. $\frac{1}{12}$
• D. $\frac{3}{4}$
• E. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{7}{12}$

If two dice are rolled total sample space $={\left(6\right)}^2=36$

Sum of face values can be a composite number
$\therefore$ Sum$=4,6,8,9,10,12$

Number of favourable cases
$=(1,3),(3,1),(2,2),(3,3),(2,4),(4,2),(5,1),(1,5),$
$(2,6),(6,2),(5,3),(3,5),(4,4),(3,6),(6,3),(4,5),(5,4),$
$(4,6),(6,4),(5,5),(6,6)=21$

Hence required probability

$=\frac{Favourablecases}{Totalnumberofcases}=\frac{21}{36}=\frac{7}{12}$