What are the odds of not rolling a three on a standard six-sided die?

Sure, let's break it down step by step:

1. Identify the total number of possible outcomes: A standard six-sided die has 6 faces, so there are 6 possible outcomes when you roll the die.

2. Identify the number of favorable outcomes: We are interested in the outcomes where we do not roll a three. The faces that are not three are 1, 2, 4, 5, and 6. So, there are 5 favorable outcomes.

3. Calculate the probability of not rolling a three: The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability of not rolling a three is: $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{6}$

4. Convert the probability to odds: The odds of an event are given by the ratio of the probability of the event occurring to the probability of the event not occurring. The probability of rolling a three is: $\text{Probability of rolling a three} = \frac{1}{6}$ Therefore, the probability of not rolling a three is: $\text{Probability of not rolling a three} = 1 - \frac{1}{6} = \frac{5}{6}$ The odds are then: $\text{Odds} = \frac{\text{Probability of not rolling a three}}{\text{Probability of rolling a three}} = \frac{\frac{5}{6}}{\frac{1}{6}} = 5$

So, the odds of not rolling a three on a standard six-sided die are 5 to 1.