Two unbiased dice are rolled once. Find the probability of getting:a) A sum 8b) A doubletc) A sum greater than 8

Let us solve the problem step by step.

Total Outcomes
When two unbiased dice are rolled, each die has 6 faces, so the total number of outcomes is: 6 × 6 = 36.

a) Probability of getting a sum of 8
The possible outcomes that give a sum of 8 are:

(2, 6)
(3, 5)
(4, 4)
(5, 3)
(6, 2)
There are 5 such favorable outcomes.

Probability = (Number of favorable outcomes) / (Total outcomes) = 5 / 36.

b) Probability of getting a doublet
A doublet occurs when both dice show the same number. The possible doublets are:

(1, 1)
(2, 2)
(3, 3)
(4, 4)
(5, 5)
(6, 6)
There are 6 such favorable outcomes.

Probability = (Number of favorable outcomes) / (Total outcomes) = 6 / 36 = 1 / 6.

c) Probability of getting a sum greater than 8
To find the outcomes where the sum is greater than 8, we consider:

Sum = 9: (3, 6), (4, 5), (5, 4), (6, 3) → 4 outcomes.
Sum = 10: (4, 6), (5, 5), (6, 4) → 3 outcomes.
Sum = 11: (5, 6), (6, 5) → 2 outcomes.
Sum = 12: (6, 6) → 1 outcome.
Total favorable outcomes = 4 + 3 + 2 + 1 = 10.

Probability = (Number of favorable outcomes) / (Total outcomes) = 10 / 36 = 5 / 18.

Final Answer
a) Probability of a sum of 8 = 5 / 36.
b) Probability of a doublet = 1 / 6.
c) Probability of a sum greater than 8 = 5 / 18.