Question

Six faces of a die are marked with number $1,-1,0,-2,2,3,$ and the die is thrown thrice. The probability that the sum of the numbers thrown is six, is

• A. $\frac{3}{216}$
• B. $\frac{9}{216}$
• C. $\frac{10}{216}$
• D. $\frac{18}{216}$

Answer 1

The correct option is B $\frac{9}{216}$

$\Rightarrow$ If a die thrown thrice then

total number of outcomes $=6^3=216$

die is marked with $1,-1,0,-2,2,3$

let $A=$ sum of numbers is nine

$=\left\{\right(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1),(3,3,0),(3,0,3),(0,3,3\left)\right\}$

$n\left(A\right)=9$

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{9}{216}$