What is the probability of rolling at least one six with one roll of a pair of dice?

To find the probability of rolling at least one six with one roll of a pair of dice, we need to know two things. First we need to know how many different possible outcomes there are when we roll the dice one time. We know that there are 36 different possible outcomes. They are 1-1, 1-2, 1-3,..., 6-4, 6-5 and 6-6.

We also need to know how many different times at least one six can appear. These will include, 1-6, 2-6, 3-6, 4-6, 5-6, 6-6, 6-1, 6-2, 6-3, 6-4, and 6-5, for a total of 11 possible outcomes with at least one six. (Note that the 6-6 possible outcome is included in the list because it fits the requirement of "at least one six" with a given single pass of the dice.

The odds of rolling at least one six in one pass with a pair of dice are 11 in 36. To find the probability of this, we need to divide the 11 by the 36, and this gives us a probability of 11/36 or 0.3055555....

Remember that probability is a ratio, and it's the ratio of the number of possible times a given outcome can appear to the total number of possible outcomes that could appear. This ratio will range from zero to one, inclusive. A probability of zero means that a given outcome cannot occur. Like rolling a 13 with one pass of a regular pair of dice. That can't happen, so the probability of it happening is zero.

We also understand that if the probability of something happening is one, then that outcome must happen. Like the probability of rolling an odd or an even number. We know that an odd or an even number must appear, so the probability of that happening is one.