What is the probability of rolling 7 or 11 with 2 dice?

Answer 1

The probability of rolling a 7 on a pair of 2 dices is: P(7) = 6/36.

The probability of rolling a 11 on a pair of 2 dices is: P(11) = 2/36.

The probability of rolling 7 or 11 is the sum of both single probabilities:

P(7 or 11) = 6/36 + 2/36 = 8/36 = 2/9 = 0.2222... ≈ 22.2%.

Explanation.

When rolling a pair of fair dice there are 36 possible equiprobable events or

outcomes. They are:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), . . . . . . . . . . . . . . . . . , (3,6),

(4,1), . . . . . . . . . . . . . . . . . , (4,6),

(5,1), . . . . . . . . . . . . . . . . . , (5,6),

(6,1), . . . . . . . . . . . . . . . . . , (6,6).

Each of these 36 events has the probability of happening of 1/36.

For the case of the sum of both dice to be 7, there are 6 possible outcomes, so the

probability of the event sum equals 7 is: P(7) = 6/36 = 1/6.

For the case of the sum of both dice to be 11, there are 2 possible outcomes, (6,5)

and (5,6), so the probability of the event sum equals 11 is: P(11) = 2/36 = 1/18.