Dice Probabilities

15 Points Per Correct Answer - No time limit  

1. Two six-sided dice are rolled. Find the probability the first die came up a 2 and the second die came up a 5. 1/18 1/9 1/12 1/36

2. Two six-sided dice are rolled. Find the probability that one die came up a 2 and the other came up a 6. 1/9 1/36 1/18 1/12

3. Two six-sided dice are rolled. Find the probability that at least one die is a 3. 1/2 11/36 1/6 1/3

4. Two six-sided dice are rolled. Find the probability that the sum is 8. 5/36 1/6 1/3 5/18

5. Two six-sided dice are rolled. Find the probability that the sum is 8 given that the first die was 3. 1/6 5/18 1/5 1/12

6. Two six-sided dice are rolled. Find the probability that the first die came up 3 given that the dice sum to 8. 1/6 1/5 1/12 5/18

7. Two six-sided dice are rolled. Find the probability that their sum is not 7. 23/36 3/4 5/6 2/3

8. Two six-sided dice are rolled. Find the probability that their sum is not 8, given that their sum is not 7. 23/36 3/4 5/6 2/3

9. Two six-sided dice are rolled. Find the probability that the first die is not a 5, given that the second die is not a 2. 29/36 2/3 5/6 25/36

10. Two six-sided dice are rolled. But this time, the dice aren't fair: For each die, a 1 is twice as likely to be rolled as a 2, a 2 is twice as likely to be rolled as a 3, ..., and a 5 is twice as likely to be rolled as a 6 (in other words, each number is twice as likely as the number that follows it). So what is the probability of rolling a sum of 7? 64/1323 64/1123 64/1223 64/1023