If a dice is rolled 3 times and the sum of the three numbers that appear is 16. Find the probability of getting 5 in the second roll.  Ops:   A. 1/108    B. 1/54    C. 3/108    D. 3/216

To solve this problem, we need to consider the total number of outcomes when a dice is rolled 3 times and the number of outcomes where the sum is 16 and the second roll is 5.

1. Total number of outcomes when a dice is rolled 3 times: Since a dice has 6 faces, the total number of outcomes when it is rolled 3 times is 6^3 = 216.

2. Number of outcomes where the sum is 16 and the second roll is 5: We need to find the number of ways to get a sum of 16 with 3 dice, where the second roll is 5. This means the sum of the first and third rolls should be 16 - 5 = 11. The possible combinations are (6,5), (5,6). So, there are 2 ways.

3. Therefore, the probability of getting 5 in the second roll when the sum of the three numbers is 16 is 2/216 = 1/108.

So, the answer is A. 1/108.

To solve this problem, we need to consider the total number of outcomes when a dice is rolled 3 times and the number of outcomes that satisfy the condition of getting a sum of 16 and a 5 in the second roll.

1. Total number of outcomes when a dice is rolled 3 times: Since a dice has 6 faces, the total number of outcomes when it is rolled 3 times is 6^3 = 216.

2. Number of outcomes that satisfy the condition: We need to find the number of ways to get a sum of 16 with a 5 in the second roll. This means we need to find the number of ways to get a sum of 11 with two dice rolls (one before and one after the second roll). The combinations are (6,5), (5,6), and (6,6). So, there are 3 ways to get a sum of 11 with two dice rolls.

Therefore, the probability of getting a sum of 16 with a 5 in the second roll is 3/216 = 1/72. However, none of the options A, B, C, D match this result. There might be a mistake in the problem or the options.