Question

A special dice with number $1,-1,2,-2,0$ and $3$ is thrown thrice. What is the probability that the sum of the number occurring on the upper face is zero?

• A. $\frac{1}{72}$
• B. $\frac{1}{8}$
• C. $\frac{7}{72}$
• D. $\frac{25}{216}$

Answer 1

Answer: (D)

$\frac{25}{216}$

The possible favourable outcomes are

$(1,-1,0)⟹6$ possibilities

$(2,-2,0)⟹6$ possibilities

$(-2,-1,3)⟹6$ possibilities

$(-1,-1,2)⟹3$ possibilities

$(1,1,-2)⟹3$ possibilities

$(0,0,0)⟹1$ possibility

Total number of favourable outcomes are $25$.

Total outcomes of 3 throws of die are $6\times 6\times 6=216$

The probability of 0 sum on top face $=\frac{25}{216}$