two fair dice are rolled, find the

A)odds of getting a 9
B) the odds against getting a 12

you can get it with a 5,4; 6,3

pr= 2*pr(5,4)+ 2*pr(6,3)= 4*1/6*1/6=1/9

against a 12, that is the same as 1-pr(12)

pr= 1-1/6*1/6= 35/36

23

If you roll a fair-sided die twice, what is the probability of getting a double?

To find the odds of getting a specific outcome when rolling dice, we need to determine the number of favorable outcomes (the outcomes that meet our condition) and the total number of possible outcomes.

A) To find the odds of getting a 9 when rolling two fair dice, we need to count the number of favorable outcomes where the sum of the two dice is equal to 9.

Possible favorable outcomes:
- (3, 6) - a 3 on the first die and a 6 on the second die
- (4, 5) - a 4 on the first die and a 5 on the second die
- (5, 4) - a 5 on the first die and a 4 on the second die
- (6, 3) - a 6 on the first die and a 3 on the second die

Total number of possible outcomes: Since we're rolling two dice, each with 6 possible outcomes, there are a total of 6 x 6 = 36 possible outcomes.

Therefore, the odds of getting a 9 are 4 favorable outcomes out of 36 possible outcomes, which can be simplified to 1:9 odds (or 1/9 probability).

B) To find the odds against getting a 12 when rolling two fair dice, we need to determine the number of unfavorable outcomes where the sum of the two dice is not equal to 12.

Possible unfavorable outcomes (where the sum doesn't equal 12):
- (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, 2), (3, 3), (3, 4), (3, 5), (3, 6)
- (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
- (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

There are a total of 36 possible outcomes, and we've listed 36 unfavorable outcomes. So, the odds against getting a 12 are 36 unfavorable outcomes out of 36 possible outcomes, which can be simplified to 1:1 odds (or 1/1 probability).

Therefore, the odds against getting a 12 are certain, meaning it is impossible to get a sum of 12 when rolling two fair dice.