Question

Two unbiased dice are rolled once. What is the probability of getting a sum less than $10$.

Answer 1

Two unbiased dice are rolled once. So, the possible outcomes are

$S=\left\{\right(1,1),(1,2),...(1,6),(2,1),...(2,6),(3,1),..(3,6),.....,(6,6\left)\right\}$

$\therefore n\left(S\right)=36$

Let $A$ be an event of getting a sum less than $10$.

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

$\therefore n\left(A\right)=30$

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{30}{36}=\frac{5}{6}$

Hence, $P\left(A\right)=\frac{5}{6}$