Two dice are thrown. What is the probability that the sum of the numbers is divisible by 3?
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
\(\frac{12}{36} = \frac{1}{3}.\)
There is an explanation video available below.
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