Two dice are thrown together. The probability that sum of the numbers is divisible by 2 or 3 is
Two dice are thrown together. The probability that sum of the numbers is divisible
by 2 or 3 is
$\frac{1}{6}$
$\frac{3}{4}$
$\frac{1}{3}$
$\frac{2}{3}$
Solution
Two dice are thrown together. Then sum of $2,3,4,6,8,9,10,12$ is obtained in following ways.
Let $A=\{(2,2),(1,2),(1,1),(1,3),(1,5),(2,1),(2,4),(2,6),(3,1),(3,3),(3,5),(3,6)$,
$(4,5),(4,2),(4,4),(4,6),(5,1),(5,3),(5,4),(5,5),(6,2),(6,3),(6,4),(6,6)\}$
Thus $n(A)=24$ and $n(S)=6 \times 6=36$
$\therefore \mathrm{P}(\mathrm{A})=\frac{\mathrm{n}(\mathrm{A})}{\mathrm{n}(\mathrm{S})}=\frac{24}{36}=\frac{2}{3}$