Question

In rolling 2 fair dice what is the probability of a sum greater than 3 but not exceeding 6

Answer 1

The probability of rolling two fair dice and getting a sum greater than 3 but not exceeding 6 is approximately 16.67%.

Step-by-step explanation:

The probability of rolling two fair dice and getting a sum greater than 3 but not exceeding 6 can be found by counting the favorable outcomes and dividing by the total number of possible outcomes.

First, let's determine the favorable outcomes:

To get a sum greater than 3 but not exceeding 6, we need to consider the following combinations: (1, 3), (2, 2), (3, 1), (2, 4), (4, 2), (3, 3). This gives us a total of 6 favorable outcomes.

Now, let's determine the total number of possible outcomes:

When rolling two dice, each die can have 6 possible outcomes. So, the total number of possible outcomes is 6 * 6 = 36.

Finally, we can calculate the probability:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 6/36 = 1/6 = 0.1667, approximately 16.67%.

Answer 2

To find the probability of a sum greater than 3 but not exceeding 6 when rolling two fair dice, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

Step-by-step explanation:

To find the probability of a sum greater than 3 but not exceeding 6 when rolling two fair dice, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. Let's analyze the various outcomes:

Sum greater than 3: The sums 4, 5, 6, 7, 8, 9, 10, 11, and 12 all satisfy this condition.Sum not exceeding 6: The sums 2, 3, 4, 5, and 6 satisfy this condition.Sum greater than 3 but not exceeding 6: The only possible sums that satisfy this condition are 4, 5, and 6.

Since we have a total of 36 possible outcomes (6 choices for the first die and 6 choices for the second die), and only 3 favorable outcomes, the probability is 3/36, which simplifies to 1/12 or 0.0833.