What is the probability of rolling a sum of 7 with two dice?

To determine the probability of rolling a sum of 7 with two six-sided dice, we first need to calculate the total number of possible outcomes when rolling two dice. Each die has 6 faces, leading to a total of 6 multiplied by 6, which equals 36 possible outcomes.

Next, we identify the combinations that yield a sum of 7. The following pairs of rolls result in this sum:

• (1, 6)

• (2, 5)

• (3, 4)

• (4, 3)

• (5, 2)

• (6, 1)

Counting these combinations, we find there are 6 different ways to roll a sum of 7.

To find the probability, we take the number of successful outcomes (which is 6) and divide it by the total number of possible outcomes (which is 36). This gives us:

[

P(\text{sum of 7}) = \frac{6}{36} = \frac{1}{6}

]

The correct choice is therefore ( \frac{1}{6} ), as it correctly represents the probability of obtaining a sum of 7 when rolling two dice. The choice that states