a fair dice is tossed twice 1 at most 6 at least 9

where is answer

Where is question?

To find the probability of obtaining a sum of 9 or more on two fair dice, we need to consider all the possible outcomes.

Let's break down the possible outcomes by listing all the ways we can get a sum of 9 or more on two dice:

1. When the first die shows a 6, we can get a sum of 9, 10, 11, or 12 with the second die. (6 + 3, 6 + 4, 6 + 5, or 6 + 6)
2. When the first die shows a 5, we can get a sum of 9, 10, 11, 12, or 13 with the second die.
3. When the first die shows a 4, we can get a sum of 9, 10, 11, 12, 13, or 14 with the second die.
4. When the first die shows a 3, we can get a sum of 9, 10, 11, 12, 13, 14, or 15 with the second die.
5. When the first die shows a 2, we can get a sum of 9, 10, 11, 12, 13, 14, 15, or 16 with the second die.
6. When the first die shows a 1, we can get a sum of 9, 10, 11, 12, 13, 14, 15, 16, or 17 with the second die.

Now, let's calculate the probabilities for each possible outcome:

For the first possible outcome, the probability is 1/6 (since there is only one way to roll a 6 on the first die) multiplied by 4/6 (since there are four possible outcomes to achieve a sum of 9 or more on the second die out of a total of six outcomes) which gives us a probability of (1/6) * (4/6) = 4/36.

Following the same logic, we can calculate the probabilities for each possible outcome:

1. Probability of getting a sum of 9 or more when the first die shows a 6: (1/6) * (4/6) = 4/36.
2. Probability of getting a sum of 9 or more when the first die shows a 5: (1/6) * (5/6) = 5/36.
3. Probability of getting a sum of 9 or more when the first die shows a 4: (1/6) * (6/6) = 6/36.
4. Probability of getting a sum of 9 or more when the first die shows a 3: (1/6) * (7/6) = 7/36.
5. Probability of getting a sum of 9 or more when the first die shows a 2: (1/6) * (8/6) = 8/36.
6. Probability of getting a sum of 9 or more when the first die shows a 1: (1/6) * (9/6) = 9/36.

Finally, we add up all the probabilities:

Total probability of getting a sum of 9 or more on two dice = (4/36) + (5/36) + (6/36) + (7/36) + (8/36) + (9/36) = 39/36.

However, probabilities cannot exceed 1, so the maximum possible probability is 1. Thus, the correct probability is 1.