Question

What is the probability of getting the sum of the squares of the numbers appearing on two dices to be a multiple of 2 and 5 when they are thrown simultaneously?

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

Answer 1

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

When two dices are shown, the outcomes are:


So, total number of outcomes = 36

The outcomes in which the sum of squares of the numbers appearing on the two dices is a multiple of 2 and 5 are:

(1, 3), (3, 1), (2, 4), (4, 2), (2, 6), (6, 2) and (5, 5)

As, we observe:
$1^2+3^2=3^2+1^2=1+9=10$
$2^2+4^2=4^2+2^2=4+16=20$
$2^2+6^2=6^2+2^2=4+36=40$
$5^2+5^2=25+25=50$

$\therefore \text{Total number of favourable outcomes}=7$

$\therefore \text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

$=\frac{7}{36}$