# Probability of Rolling Sum > 3 with Two Dice

• MHB
• anyalong18
In summary, the probability of rolling a sum greater than 3 with two dice is approximately 83.33%, or 5/6. To calculate the probability, you can use the formula: (Total number of possible outcomes with a sum greater than 3) / (Total number of possible outcomes with two dice). In this case, there are 36 possible outcomes with two dice and 30 possible outcomes with a sum greater than 3, giving you a probability of 30/36 or 5/6. The probability of rolling a specific number for the sum is 6/36 or 1/6. This is because there are 6 possible ways to roll a 7 with two dice (1+6,
anyalong18
Two fair dice are rolled. What is the probability of rolling a sum that exceeds 3?

skeeter said:
is it 1/36

a sum that exceeds 3 is a sum $\ge$ 4

When rolling two dice the possible sums are 1+ 1= 2 to 6+ 6= 12. The specific possible outcomes are
1+ 1= 2
1+ 2= 3
1+ 3= 4
1+ 4= 5
1+ 5= 6
1+ 6= 7
2+ 1= 3
2+ 2= 4
2+ 3= 5
2+ 4= 6
2+ 5= 7
2+ 6= 8
3+ 1= 4
3+ 2= 5
3+ 3= 6
3+ 4= 7
3+ 5= 8
3+ 6= 9
4+ 1= 5
4+ 2= 6
4+ 3= 7
4+ 4= 8
4+ 5= 9
4+ 6= 10
5+ 1= 6
5+ 2= 7
5+ 3= 8
5+ 4= 9
5+ 5= 10
5+ 6= 11
6+ 1= 7
6+ 2= 8
6+ 3= 9
6+ 4= 10
6+ 5= 11
6+ 6= 12

A total of 6x6= 36 outcomes, not all different.

Now, how many of those "exceed 3" (i.e. are 4 or higher)? The probability of exceeding 3 is that number divided by 36.

You might find it simpler to count the number of rolls that give "2" or "3" and subtract that from 36.

## 1. What is the probability of rolling a sum greater than 3 with two dice?

The probability of rolling a sum greater than 3 with two dice is 11/12 or approximately 0.917. This means that there is a 91.7% chance of rolling a sum greater than 3 when rolling two dice.

## 2. How is the probability of rolling a sum greater than 3 calculated?

The probability of rolling a sum greater than 3 is calculated by finding the number of possible outcomes that result in a sum greater than 3 and dividing it by the total number of possible outcomes when rolling two dice. In this case, there are 36 possible outcomes when rolling two dice (6 possible outcomes for each die), and 33 of those outcomes result in a sum greater than 3 (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12). Therefore, the probability is 33/36 or 11/12.

## 3. Can the probability of rolling a sum greater than 3 change?

Yes, the probability of rolling a sum greater than 3 can change depending on the number of dice being rolled. For example, if three dice are rolled, the probability of rolling a sum greater than 3 increases to 125/216 or approximately 0.579. This is because there are more possible outcomes that result in a sum greater than 3 when rolling three dice compared to two dice.

## 4. What is the probability of rolling a specific sum, such as 7, with two dice?

The probability of rolling a specific sum, such as 7, with two dice is 1/6 or approximately 0.167. This is because there are 6 possible outcomes that result in a sum of 7 when rolling two dice (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1), and there are 36 total possible outcomes.

## 5. How does the probability of rolling a sum greater than 3 with two dice relate to the individual probabilities of each die?

The probability of rolling a sum greater than 3 with two dice does not directly relate to the individual probabilities of each die. However, the individual probabilities of each die can be used to calculate the overall probability. For example, the probability of rolling a sum greater than 3 with two dice can be calculated by multiplying the probability of rolling a 1 on one die (1/6) with the probability of rolling a 2 on the other die (1/6). This results in a probability of 1/36, which is one of the 33 possible outcomes that result in a sum greater than 3 (1+2). Therefore, the individual probabilities can be used to calculate the overall probability, but they do not directly relate to it.

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