what is the difference between 5/6 and 1/6 in probability ?

In probability, the difference between \(\frac{5}{6}\) and \(\frac{1}{6}\) can be understood by examining the context in which these fractions are used.

1. **Numerical Difference**:
   \[
   \frac{5}{6} - \frac{1}{6} = \frac{5 - 1}{6} = \frac{4}{6} = \frac{2}{3}
   \]
   The numerical difference between \(\frac{5}{6}\) and \(\frac{1}{6}\) is \(\frac{2}{3}\).

2. **Interpretation in Probability**:
   - **\(\frac{5}{6}\)**: This represents a high probability event, occurring 5 times out of 6 trials.
   - **\(\frac{1}{6}\)**: This represents a low probability event, occurring 1 time out of 6 trials.

3. **Contextual Understanding**:
   - In a fair six-sided die, the probability of rolling a specific number (say 1) is \(\frac{1}{6}\).
   - The probability of rolling any number except 1 (i.e., 2, 3, 4, 5, or 6) is \(\frac{5}{6}\).

4. **Complementary Probabilities**:
   - The events represented by \(\frac{5}{6}\) and \(\frac{1}{6}\) are complementary. This means that the sum of their probabilities is 1:
     \[
     \frac{5}{6} + \frac{1}{6} = 1
     \]
   - \(\frac{5}{6}\) is the probability of the complement of the event with probability \(\frac{1}{6}\).

To summarize, the difference between \(\frac{5}{6}\) and \(\frac{1}{6}\) in probability highlights the contrast between a high probability event and a low probability event, where \(\frac{5}{6}\) is significantly more likely to occur than \(\frac{1}{6}\).

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. What is the difference between theoretical probability and experimental probability?
2. How do you calculate the probability of complementary events?
3. What is the probability of rolling a number greater than 4 on a fair six-sided die?
4. How do you find the probability of multiple independent events?
5. What is the difference between conditional probability and joint probability?
6. How do you use probability to determine the odds of an event?
7. What is the role of probability in statistics?
8. How do you calculate the expected value of a probability distribution?

**Tip:** In probability, always ensure the sum of the probabilities of all possible outcomes of an event equals 1.

Explore the difference between \(\frac{5}{6}\) and \(\frac{1}{6}\) in probability. Learn how to calculate the numerical difference, interpret these probabilities in various contexts, and understand complementary probabilities. Suitable for high school students.

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