When rolling two 6-sided dice, what is the probability of rolling a sum of 7 and 11?

We have two 6-sided dice.

Each one of them has 6 possible outcomes.

The total number of outcomes for the pair, will be equal to the product between the numbers of outcomes for each one of them

Then the total number of outcomes is:

C = 6*6 = 36.

The number of outcomes where the sum of the dice are 7 are:

1 and 6

6 and 1

2 and 5

5 and 2

3 and 4

4 and 3

So we have 6 outcomes where the sum of both numbers is equal to 7.

The probability of rolling a pair such that the sum is equal to 7, is equal to the quotient between the number of outcomes that meet this condition (6) and the total number of outcomes (36)

The probability is:

P = 6/36 = 1/6

Now let's do the same for 11.

The outcomes where the sum is 11 are:

5 and 6

6 and 5

So we have two outcomes.

In this case, the probability will be:

P = 2/36 = 1/18

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