Question

Two fair dice are thrown simultaneously. The probability of getting the sum of numbers shown on the dice is either divisible by 2 or divisible by 5, is

• A. $\frac{2}{3}$
• B. $\frac{13}{18}$
• C. $\frac{7}{12}$
• D. $\frac{11}{18}$

Answer 1

The correct option is D $\frac{11}{18}$

Total number of outcomes when two fair dice are rolled = 36
Outcomes having the sum on the dice either divisible by 2 or by 5:
(1, 1), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 6), (3, 1), (3, 2), (3, 3), (3, 5), (4, 1), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)
$\therefore \text{Number of favourable outcomes}=22$$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{22}{36}$
$=\frac{11}{18}$
Hence, the correct answer is option (d).