Explanation:
After a red 3, the highest possible sum is 3 + 6 = 9.
So P(sum ≥ 10) = 0 after a red 3 has occurred.
There are 5 ways the sum can be greater than or equal to 10 (4 and 6, 6 and 4, 5 and 5, 5 and 6, 6 and 5). There are a total of 36 possible permutations. Therefore:
P(sum ≥ 10) = 5/36
The conditional probability is:
P(sum ≥ 10 | red 3) = P(sum ≥ 10 AND red 3) / P(red 3)
P(sum ≥ 10 | red 3) = 0 / (1/6)
P(sum ≥ 10 | red 3) = 0