Question

Two dice are thrown simultaneously. The probability of sum of the cubes of the numbers on the top of the dice is a perfect square number is

• A. $\frac{1}{9}$
  
• B. $\frac{1}{8}$
  
• C. $\frac{1}{12}$
  
• D. $\frac{1}{6}$
  

Answer 1

The correct option is C $\frac{1}{12}$


Total number of outcomes, when two dice are thrown = 36
Sum of cubes of the numbers on the top of dice which is a perfect square number are (1, 2), (2, 1) and (2, 2).
As, $2^3+1^3=8+1$
$=9=3^2$
Also, $2^3+2^3=8+8$
$=16=4^2$
Total number of favourable outcomes = 3
$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{3}{36}$
$=\frac{1}{12}$
Hence, the correct answer is option (c).