Question

Two dice are thrown simultaneously. The probability that the sum of squares of the numbers shown on the dice is a multiple of 2 and 5, is

• A. $\frac{1}{9}$
  
• B. $\frac{1}{16}$
  
• C. $\frac{7}{36}$
  
• D. $\frac{5}{18}$
  

Answer 1

The correct option is C $\frac{7}{36}$


Total number of outcomes when two dice are thrown = 36
Outcomes in which the sum of squares of the numbers is a multiple of 2 and 5:
(1, 3), (3, 1), (2, 4), (4, 2), (2, 6), (6, 2) and (5, 5)
As, $1^2+3^2=1+9=10$
$2^2+4^2=4+16=20$
$2^2+6^2=4+36=40$
$5^2+5^2=25+25=50$
$\therefore \text{Total number of favourable outcomes}=7$
$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{7}{36}$
Hence, the correct answer is option (c).