Question

Two different dice are tossed together. Find the probability:
(i) of getting a doublet
(ii) of getting a sum $10$, of the number on the two dice.

Answer 1

When two dice are tossed together,

Total possible outcomes $=6^2=36$.

$\left(i\right)P\left(doublet\right):$

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

Number of favorable outcomes $=6$

$\therefore$ Probability of getting a doublet $=P\left(doublet\right)=\frac{6}{36}=\frac{1}{6}.$

$\left(ii\right)P(sum=10):$

The favourable outcomes $=\left\{\right(4,6),(5,5),(6,4\left)\right\}$

Number of favorable outcomes $=3$

$\therefore$ Probability of getting a sum 10 $=P(sum=10)=\frac{3}{36}=\frac{1}{12}.$