A traditional number cube, also known as a six-sided die, has six faces numbered from 1 to 6. When rolling the die, each face has an equal probability of landing face-up.
When rolling a die twice, we can analyze the probabilities of the two rolls separately, since the outcome of the first roll does not affect the outcome of the second roll.
The probability of any specific outcome on a single roll of a die is:
\[ P(\text{specific number}) = \frac{1}{6} \]
When rolling the die twice, there are a total of \(6 \times 6 = 36\) possible outcomes (since there are 6 outcomes for the first roll and 6 outcomes for the second roll).
Examples of Outcomes
If we were to record the outcomes of two rolls, it would look something like:
- (1, 1)
- (1, 2)
- (1, 3)
- ...
- (6, 6)
Summary of Scenarios
- Total outcomes when rolling twice: \(36\)
- Probability of any specific outcome (e.g., rolling a (4, 5) or (2, 2)):
\[ P(\text{specific outcome}) = \frac{1}{36} \]
- The probability of getting any particular outcome in the first roll does not affect the outcomes of the second roll.
To summarize, the probability model for rolling a traditional number cube (die) twice involves understanding that there are 36 different combinations of results when rolling a die two times. The individual probabilities for specific sequences of rolls can be calculated based on the total outcomes.
If you have a specific event or situation in mind regarding rolling the die twice (e.g., both rolls being the same, rolling a specific pair, etc.), please provide that, and I can help calculate that specific probability!
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