Answer:
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
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