Two dice are thrown. What is the probability that the sum of the numbers is divisible by 3?
A
\(\frac{1}{4}\)
B
\(\frac{2}{3}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{3}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
The two dice produce 36 equally likely outcomes in total.
The sums divisible by 3 are exactly 3, 6, 9, and 12. The complete list of favorable pairs \((d_1, d_2)\) is:
Sum = 3 (2 ways):
(1,2), (2,1)
Sum = 6 (5 ways):
(1,5), (2,4), (3,3), (4,2), (5,1)
Sum = 9 (4 ways):
(3,6), (4,5), (5,4), (6,3)
Sum = 12 (1 way):
(6,6)
Total favourable outcomes: 2 + 5 + 4 + 1 = 12.
Therefore, the probability is
\(\frac{12}{36} = \frac{1}{3}.\)
Source: Myschool Past Questions Archive (Record #33110)