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When dealing with probability in dice games, it's important to understand what constitutes a favorable outcome. Imagine you have a standard six-sided die. Each number, from 1 to 6, is printed on a different side. In our example, we're tasked with finding the probability of rolling either a 2 or a 3. These are our **favorable outcomes** because they are the specific results we are interested in.

It's similar to picking the winning numbers in a lottery, only that here we focus on a smaller pool. For our scenario:

• The favorable outcome of rolling a 2 is that a 2 appears on top when the die comes to a rest.
• Similarly, rolling a 3 also counts as a favorable outcome.

In total, there are 2 favorable outcomes for our exercise.

Total possible outcomes refer to all the different results you could achieve when rolling a die. A standard six-sided die has exactly six faces, each displaying a different number from 1 to 6.

Whenever you roll the die, each of these sides has an equal chance of facing up. Therefore, the total possible outcomes when rolling a single die are:

• 1
• 2
• 3
• 4
• 5
• 6

Understanding this total is crucial because it gives us a complete set of outcomes that we'll use in our probability calculation. In this exercise, our total possible outcomes are 6.

Now that we've identified our favorable outcomes and total possible outcomes, we can calculate probability. Probability measures how likely an event is to occur, and it's expressed as a fraction. The formula is simple:\[\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}}\]For our die-tossing example, we have 2 favorable outcomes (rolling a 2 or a 3) and 6 total possible outcomes (each side of the die). Plug these numbers into our formula: \[\text{Probability} = \frac{2}{6}\]Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2.\[\text{Probability} = \frac{1}{3}\]So, the probability of rolling a 2 or a 3 on a single toss of a six-sided die is \(\frac{1}{3}\), which means you have a one in three chance of these numbers coming up.