Question

Two unbiased dice are thrown $3$ times. Find the probability that the sum nine would be obtained once.

Answer 1

Two dice is thrown $3$ times sum would be $9$ in cases $(5,4),(4,5),(3,6)$ and $(6,3)$ assuming $6$faces in dice so $4$ times sum $9$ would occur, if $3$ times probability is $\frac{1}{6}\times \frac{1}{6}\times \frac{1}{6}=\frac{1}{216}$

$9$ occuring once $=\frac{4}{216}=\frac{1}{54}$

$9$ occuring twice $\frac{4+4}{216}=\frac{8}{216}=\frac{1}{27}$