Question

Two dice are thrown together then the probability that the sum of the number on the two faces is divisible by 4 or 6 is_________

• A. $\frac{5}{18}$
• B. $\frac{13}{18}$
• C. $\frac{7}{18}$
• D. $\frac{17}{18}$

Answer 1

The correct option is C $\frac{7}{18}$

(c)

$Clearly,n\left(S\right)=6\times 6=36$

Let E be the event that the sum of the numbers on the two faces is divisible by 4 or 6. Then,

$E=\left\{\right(1,3),(1,5),(2,2),(2,4),(2,6\left)\right(3,1\left)\right(3,3),(3,5\left)\right(4,2),(4,4),(5,1),(5,3),(6,2),(6,6\left)\right\}$


$\therefore n\left(E\right)=14$
$Hence,P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{14}{36}=\frac{7}{18}$