You roll two six-sided dice. Match each event with its probability.

The sum is 8 or 11.

The sum is 12 or less than 10.

The sum is 3 or less than 3.

The sum is 2 or 10.

A) probability the sum is 8 or 11 = 4/21

B) probability that sum is 12 or less than 10 = 6/7

C) Probability that the sum is 3 or less than 3 = 2/21

D) Probability that the sum is 2 or 10 = 1/7

Step-by-step explanation:

Since we have the same probability of each event in each dice, the answer would be just to check the different outcomes, two dices, each with 1 to 6;

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

Thus, there are 21 possible outcomes.

Now,

A) probability that the sum is 8 or 11;

From the outcomes above, the number of outcomes that have a sum as 8 or 11 are;

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

So, probability = 4/21

B) From the outcomes above, the number of outcomes that are 12 or less than 10 are;

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

There are 18 possible outcomes.

So, probability that sum is 12 or less than 10 = 18/21 = 6/7

C) From the initial 21 outcomes, the number of outcomes that the sum is 3 or less than 3 are; (1,1); (1,2)

Thus,

Probability that the sum is 3 or less than 3 = 2/21

D) From the initial 21 outcomes, the number of outcomes that the sum is 2 or 10 are;

(1,1); (4,6); (5,5)

Thus,

Probability that the sum is 2 or 10 = 3/21 = 1/7