Question

If you roll two different numbered cubes, then what is the probability that the number formed by adding the numbers on the cubes is divisible by 3?

• A. $\frac{1}{5}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{3}$


From the given sample space:
The total number of possible outcomes $=36$
1 and 2 makes 12, which is divisible by 3.
Similarly, all the possible 2-digit numbers that can be formed by throwing two different cubes are $(12,15,21,24,33,36,42,45,51,54,63,66)$
Number of favorable outcomes $=12$
Probability of the 2-digit number formed by the cubes is divisible by $3=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{12}{36}=\frac{1}{3}$