Question

Two dice are thrown simultaneously. The probability that the sum of numbers on the faces is divisible by 4 or 6 will be

• A.
  $\frac{5}{19}$
• B.
  $\frac{3}{14}$
• C.
  $\frac{1}{13}$
• D.
  $\frac{7}{18}$

Answer 1

The correct option is D

$\frac{7}{18}$
When two dice are thrown simultaneously, the total number of possible outcomes is $6^2=36.$
Let A be the event that the sum of numbers on two faces is divided by 4 or 6.

Thus, the favourable outcomes are
(1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1),
(3, 3), (3, 5), (4, 2), (4, 4), (5, 1), (5, 3), (6, 2), (6, 6).

Thus, the number of favourable outcomes is 14.

$P\left(A\right)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{14}{36}=\frac{7}{18}$

Hence, the correct answer is option d.