Question

Two cubical dice are thrown simultaneously. Find the probability of getting an even number of first dice or getting the sum $9$ on two dice.

Answer 1

Throwing two dimensional no. of events $=6^2=36$

Let $A$ be the event of getting even no, and $B$ be the event of getting sum $9$.

Then

$A=\left\{\right(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,2),(6,4),(6,6\left)\right\}$

$n\left(A\right)=9$

$P\left(A\right)=\frac{n\left(A\right)}{n\left(5\right)}=\frac{9}{36}=\frac{1}{4}$

$B=\left\{\right(3,6),(4,5),(5,4),(6,3\left)\right\}$

$n\left(B\right)=4$

$P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{4}{36}=\frac{1}{9}$

Since $A$ and $B$ are mutually exclusive,

$P(A\cup B)=P\left(A\right)+P\left(B\right)=\frac{1}{4}+\frac{1}{9}=\frac{13}{36}$