Two dice are thrown simultaneously. The probability that the sum of th...
Solution:
When two dice are thrown simultaneously, the total number of outcomes = 6 x 6 = 36.
We need to find the probability that the sum of the numbers obtained is divisible by 7.
Let's list all possible outcomes of throwing two dice:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Now, let's find the pairs of outcomes whose sum is divisible by 7:
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
There are 6 such pairs of outcomes.
Therefore, the required probability = 6/36 = 1/6.
Therefore, option 'A' is the correct answer.