Question

A special die with numbers $1,-1,2,-2,0$ and $3$ is thrown thrice. What is the probability that the total is zero?

• A. $\frac{25}{216}$
• B. $\frac{1}{6}$
• C. $\frac{1}{9}$
• D. $\frac{1}{12}$

Answer 1

The correct option is A $\frac{25}{216}$

Total is zero so possible Cases:
$(-1,1,0)⟹P\left(I\right)={\frac{1}{6}}^3\times 3!=\frac{1}{36}$
$(-2,2,0)⟹P\left(II\right)={\frac{1}{6}}^3\times 3!=\frac{1}{36}$
$(0,0,0)⟹P\left(III\right)={\frac{1}{6}}^3=\frac{1}{216}$
$(3,-2,-1)⟹P\left(IV\right)={\frac{1}{6}}^3\times 3!=\frac{1}{36}$
$(-2,1,1)⟹P\left(V\right)={\frac{1}{6}}^3\times 3!=\frac{1}{36}$
Total Probability = $\frac{25}{216}$