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A Basic Problem
A basic probability problem with a six-sided die is to determine how likely it is to roll any particular number. The formula for determining the probability in this instance is to take the number of different ways that a particular thing could possibly happen, and to divide it by the number of different things that could possibly happen. When you roll a six-sided die, there are only six things that could possibly happen: you could roll a 1, 2, 3, 4, 5 or 6. There is only one way to roll any number; you can only roll a 1 by rolling a 1. So, if we divide the number of ways the outcome could occur (1) by the number of outcomes that could occur (6) we get a probability of 1 in 6 for rolling any particular number.
Four Rolls
If a six-sided die is rolled four times in a row, what are the odds of rolling the same number every time? The formula for solving this probability problem is to multiply the individual probabilities by the number of rolls. We know that the odds of rolling any particular number are 1 in 6, and we are rolling four times, so we need to multiply 1/6 by 1/6 by 1/6 by 1/6. The result of this calculation is 1 in 1296, so those are the odds of rolling the same number all four times.
Even or Odd
To determine the odds of rolling an even number or an odd number with a six-sided die, you would first consider the number of possible outcomes (which is 6) and then the number of outcomes matching the definition you have chosen. Since there are three even numbers on a six-sided die (2, 4 and 6) and three odd numbers (1, 3 and 5) this number is 3. Then you divide the number matching your definition (3) by the total number of possible outcomes (6). The result is 1 in 2, so there is a fifty-percent chance of rolling an even number and a fifty-percent chance of rolling an odd number.
A Number Smaller Than Three
The same formula can be used to show not only the probability of rolling an even number on a six-sided die, but the odds of rolling a number smaller or larger than some other number. For instance, if you want to know the odds of rolling a number smaller than three, you would first determine the number of possible ways to roll such a number on a six-sided die and then divide this number by the number of possible outcomes from rolling a six-sided die. Since there are 2 possible ways to roll a number smaller than 3 (you could roll a 1 or a 2) and 6 possible numbers that you could roll, the answer is 2 out of 6, or a 1 in 3 chance of rolling a number smaller than 3.