Question

If two dice are rolled simultaneously , then what is the probability that the sum of numbers is a multiple of either 2 or 7?

• A. $\frac{2}{3}$
• B. $\frac{23}{36}$
• C. $\frac{11}{18}$
• D. $\frac{7}{12}$

Answer 1

The correct option is A $\frac{2}{3}$

Total number of outcomes = 36

Outcomes where the sum of numbers is a multiple of 2
= {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6).

Outcomes where the sum of numbers is a multiple of 7 = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}

Total number of favourable outcomes = 18+6 = 24

For an event $E,$$\text{Probability P(E)}=\frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$

P(sum of numbers is multiple of either 2 or 7 ) $=\frac{24}{36}=\frac{2}{3}$