Understanding the Probability of Rolling Two Dice to Get a Sum of 7

When rolling two six-sided dice, there are a total of 36 possible outcomes. This is because each die has 6 faces, and the outcomes can be combined. To calculate the probability of obtaining a specific sum, such as 7, we need to first determine how many combinations of the dice can produce that sum.

Combinations That Result in a Sum of 7

Here are the pairs of dice rolls that will give us a sum of 7:

• Die 1: 1, Die 2: 6
• Die 1: 2, Die 2: 5
• Die 1: 3, Die 2: 4
• Die 1: 4, Die 2: 3
• Die 1: 5, Die 2: 2
• Die 1: 6, Die 2: 1

Counting these combinations, we see that there are 6 ways to achieve a sum of 7 when rolling two dice.

Calculating the Probability

The probability can be calculated using the formula:

Probability (P) = (Number of favorable outcomes) / (Total number of outcomes)

In our case, the number of favorable outcomes (rolling a sum of 7) is 6, and the total number of outcomes when rolling two dice is 36. Therefore, we can write:

P(rolling a sum of 7) = 6 / 36

This fraction simplifies to:

P(rolling a sum of 7) = 1 / 6

Conclusion

So, the probability of rolling two dice and getting a sum of 7 is approximately 16.67%. This means that if you roll a pair of dice multiple times, one out of every six attempts, on average, will result in a sum of 7. Happy rolling!