Real-World Examples of Probability Using One Die

📚 Quick Study Guide

• 🎲 Basic Probability: Probability is the chance of an event occurring. It's calculated as: $P(event) = \frac{Number\ of\ favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$.
• 🔢 One Die: A standard die has 6 faces, numbered 1 to 6. Each face has an equal chance of being rolled.
• ➕ Calculating Probabilities:
  • The probability of rolling a specific number (e.g., a 4) is $\frac{1}{6}$.
  • The probability of rolling an even number (2, 4, or 6) is $\frac{3}{6} = \frac{1}{2}$.
  • The probability of rolling a number greater than 4 (5 or 6) is $\frac{2}{6} = \frac{1}{3}$.
• 💡 Key Terms:
  • Event: A specific outcome or set of outcomes.
  • Sample Space: The set of all possible outcomes.

🧪 Practice Quiz

1. What is the probability of rolling a 3 on a standard six-sided die?

   1. $\frac{1}{2}$
   2. $\frac{1}{3}$
   3. $\frac{1}{6}$
   4. $\frac{5}{6}$

2. What is the probability of rolling an even number on a standard six-sided die?

   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$

3. What is the probability of rolling a number greater than 4 on a standard six-sided die?

   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$

4. What is the probability of rolling a number less than 3 on a standard six-sided die?

   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$

5. What is the probability of rolling a 7 on a standard six-sided die?

   1. $\frac{1}{6}$
   2. $\frac{1}{2}$
   3. $0$
   4. $1$

6. What is the probability of rolling a number that is either 1 or 6 on a standard six-sided die?

   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$

7. What is the probability of rolling a prime number (2, 3, or 5) on a standard six-sided die?

   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$