Answer:

Explanation:

The correct answer is option 'D'.

a) 5/6
b) 1/6
c) 1/36
d) 5/6

To solve this problem, we need to use the concept of conditional probability.

Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we are given that one of the dice rolls is a 4.

Let's use the notation P(A|B) to represent the conditional probability of event A given that event B has occurred.

We need to find the probability that the sum of the two dice is greater than 8 given that one of the dice rolls is a 4.

Let A be the event that the sum of the two dice is greater than 8, and B be the event that one of the dice rolls is a 4.

We want to find P(A|B).

To calculate P(A|B), we can use Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of event B given that event A has occurred, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.

We know that P(B) = 5/36, since there are 5 ways to get at least one 4 when rolling two dice (44, 45, 46, 54, 64) out of a total of 36 possible outcomes.

To find P(A), we need to count the number of ways to get a sum greater than 8 when rolling two dice. There are 21 such outcomes (56, 65, 66, 46, 55, 56, 66, 15, 24, 25, 26, 34, 35, 36, 44, 45, 46, 55, 56, 66). Therefore, P(A) = 21/36.

To find P(B|A), we need to count the number of outcomes where one of the dice rolls is a 4 given that the sum is greater than 8. There are 4 such outcomes (46, 56, 64, 65). Therefore, P(B|A) = 4/21.

Plugging in these values, we get:

P(A|B) = (4/21) * (21/36) / (5/36) = 4/5

Therefore, the probability that the sum of the two dice is greater than 8 given that one of the dice rolls is a 4 is 4/5, which is option D.