Question

Three dice are thrown simultaneously. What is the probability of getting 15 as the sum ?

Answer 1

Three dice are thrown so total number of outcomes-

$\therefore n\left(S\right)=6\times 6\times 6=216$

let, $A$ be the event of getting sum as $15$

Therefore total number of favorable outcomes

$A=(3,6,6),(4,6,5),(5,6,4),(6,6,3),(6,3,6),(6,4,5),(6,5,4),(4,5,6),(5,5,5),(5,4,6)$

$\therefore P\left(A\right)=\frac{\text{Number of favotable outcomes}}{\text{Total number of outcomes}}=\frac{10}{216}$

Or $P\left(A\right)=\frac{5}{108}$