Question

Two dice are thrown at the same time. Find the probability of getting:
(i) Same number on both dice (ii) Different number on the both dice.

Answer 1

(i) Two dice are thrown at the same time, now for the probability of getting some no on both dice.

$\Rightarrow A$ There is no more than $6$ way.

i.e, $A\left\{\right(1,1),(2,2),(3,3),(4,4),(5,5\left)\right(6,6\left)\right\}$

$P\left(A\right)=\frac{6}{36}=\frac{1}{6}$

(i) Two dice are thrown at the some time, now for the probability of getting different no on both dice.

$\Rightarrow B$ There is no more than $6$ way.

i.e, $A\left\{\right(1,1),(1,2),(1,3),(1,4),(1,5\left)\right(1,6)........,(6,2),(6,3),(6,4),(6,5\left)\right\}$

$P\left(B\right)=\frac{60}{36}=\frac{5}{6}$

$P\left(B\right)=1-P\left(A\right)=1-\frac{1}{6}=\frac{5}{6}$