What is the theoretical probability of rolling a factor of 6 on a die?

Answer 1

When rolling a die, a 1, or a 2, or a 3, or a 4, or a 5, or a 6 will come up. Factors of six are 1, 2, 3 and 6. This leaves 4 and 5 that are not factors of 6. The probability of rolling any one number in one roll of the die is 1 in 6, or 1/6. To find a "cumulative" probability where we "combine" the odds of rolling several numbers, as is the case here, we simply add the probability of rolling each number together and sum them.

In the case here, the probability of rolling 1 is 1/6, and the probability of rolling 2 is also 1/6, and the probability of rolling 3 is 1/6 and the probability of rolloing 6 is 1/6. We add 1/6 + 1/6 + 1/6 + 1/6 and get 1+1+1+1/6, which is 4/6. The 4/6 reduces to 2/3, and that 2/3 represents the probability of rolling a factor of 6 with one roll of a die. There is one more little thing.

Probability is a mathematical term where "odds" are expressed on a scale of zero (0) to one (1). The probability of something happening is either 0, or 1, or something in between. If the probability of something happening is 100% (which is to say that somehting must occur), then the probability is 1. And if something cannot happen, then the probability of it occurring is 0. In this light, the 2/3 chance of rolling a factor of 6 with one roll of a die is 0.6666....