Each number (8 to 13) has an equal probability of \( \frac{1}{6} \) when rolling a balanced 6-sided die.
Certainly! When rolling a balanced 6-sided die with integers 8, 9, 10, 11, 12, and 13, each outcome represents an event, and the probability distribution showcases the likelihood of each event occurring.
For a fair die, the probability of rolling any specific number is \( \frac{1}{\text{total possible outcomes}} \). Here, there are 6 possible outcomes when rolling the die, so each outcome's probability is \( \frac{1}{6} \).
Creating a probability distribution table involves listing the outcomes and their corresponding probabilities:
Outcome Probability
8 1/6
9 1/6
10 1/6
11 1/6
12 1/6
13 1/6
In this distribution table, each outcome from rolling the die is listed along with its associated probability. As the die is fair, every number from 8 to 13 has an equal chance of appearing, represented by the probability \( \frac{1}{6} \) for each outcome.
This table demonstrates that when rolling this particular 6-sided die, the probabilities for obtaining any specific number within the range 8 to 13 are all identical, indicating a uniform distribution due to the die being balanced and fair.