Question

Two dice are thrown together. What is the probability of a combination in which the sum of the numbers on the two faces is divisible by 4 or 6?

• A. $\frac{2}{9}$
• B. $\frac{7}{18}$
• C. $\frac{1}{2}$
• D. $\frac{5}{18}$

Answer 1

The correct option is B $\frac{7}{18}$


This table shows the list of possible outcomes when two dice are thrown and the sum of the values on their faces.
The numbers which are divisible by 4 or 6 are:- 4,6,8 and 12.
The cases in which these sums can be obtained 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)}
Number of favourable outcomes, $P(S=4or6)=14$
Total number of outcomes, $P\left(Total\right)=36$
Required probability = $\frac{P(S=4or6)}{P\left(Total\right)}=\frac{14}{36}=\frac{7}{18}$