When two fair dice are tossed, the probability of getting a specific sum is dependent on the number of possible outcomes that result in that sum. There are a total of 36 possible outcomes when two dice are tossed (6 sides on each die), and each sum can be achieved in a unique combination of two numbers on the dice.
If two fair dice are tossed, what is the probability that the sum is i, i = 2, 3, ... , 12?
For example, the sum of 2 can only be achieved by rolling a 1 on one die and a 1 on the other die, which has a probability of 1/36 or 2.78%. The sum of 3 can be achieved by rolling a 1 on one die and a 2 on the other die, or a 2 on one die and a 1 on the other die, which has a probability of 2/36 or 5.56%.
The probability of getting each sum when two fair dice are tossed is as follows:
Sum of 2: 1/36 or 2.78%
Sum of 3: 2/36 or 5.56%
Sum of 4: 3/36 or 8.33%
Sum of 5: 4/36 or 11.11%
Sum of 6: 5/36 or 13.89%
Sum of 7: 6/36 or 16.67%
Sum of 8: 5/36 or 13.89%
Sum of 9: 4/36 or 11.11%
Sum of 10: 3/36 or 8.33%
Sum of 11: 2/36 or 5.56%
Sum of 12: 1/36 or 2.78%
It can be observed that the probability of getting a specific sum decreases as the sum increases, and also the probability of getting a specific sum is symmetric around the sum 7.
In conclusion, understanding the probability of getting a specific sum when two fair dice are tossed is important in games and gambling where dice are used. "By knowing the probability of getting a specific sum, you can make more informed decisions and improve your chances of winning."
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