Final answer:
The probability of getting a total of 3 when rolling a pair of fair dice is 1/18. The probability of getting at most a total of 10 is 31/36.
Step-by-step explanation:
The probability of getting (a) a total of 3 when a pair of fair dice is tossed is 2/36, which simplifies to 1/18. To find this probability, we need to determine the number of favorable outcomes (rolls that result in a total of 3) and divide it by the total number of possible outcomes.
There is only one way to get a total of 3, which is by rolling a 1 on one die and a 2 on the other. Since each die has 6 sides, the total number of possible outcomes is 6*6 = 36. Therefore, the probability of getting a total of 3 is 1/18.
(b) To find the probability of getting at most a total of 10, we need to determine the number of favorable outcomes (rolls that result in a total of 10 or less) and divide it by the total number of possible outcomes.
To count the favorable outcomes, we can list all the possible combinations that result in a total of 10 or less:
- 1 + 1 = 2
- 1 + 2 = 3
- 1 + 3 = 4
- 1 + 4 = 5
- 2 + 1 = 3
- 2 + 2 = 4
- 2 + 3 = 5
- 3 + 1 = 4
- 3 + 2 = 5
- 4 + 1 = 5
- 6 + 4 = 10
- 5 + 1 = 6
- 4 + 2 = 6
- 5 + 2 = 7
- 6 + 3 = 9
- 3 + 3 = 6
- 4 + 3 = 7
- 5 + 3 = 8
- 6 + 2 = 8
- 6 + 1 = 7
- 4 + 4 = 8
- 5 + 4 = 9
- 6 + 5 = 11
- 5 + 5 = 10
- 4 + 5 = 9
- 3 + 4 = 7
- 2 + 5 = 7
- 3 + 5 = 8
- 2 + 6 = 8
- 1 + 5 = 6
- 1 + 6 = 7
Counting all the favorable outcomes, we can see that there are 31. Since the total number of possible outcomes is still 36, the probability of getting at most a total of 10 is 31/36.