Theoretical Probability Examples with Dice and Coins

📚 Quick Study Guide

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• Theoretical Probability: The likelihood of an event occurring based on mathematical calculations, assuming all outcomes are equally likely.
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• Dice Probability: With a fair six-sided die, the probability of rolling any specific number (1-6) is $\frac{1}{6}$.
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• Coin Probability: For a fair coin, the probability of getting heads (H) is $\frac{1}{2}$, and the probability of getting tails (T) is also $\frac{1}{2}$.
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• Independent Events: Events where the outcome of one does not affect the outcome of the other. The probability of both independent events A and B happening is $P(A \text{ and } B) = P(A) \times P(B)$.
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• Calculating Probability: $P(Event) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

🧪 Practice Quiz

1. What is the theoretical probability of rolling a 4 on a fair six-sided die?
   1. $\frac{1}{2}$
   2. $\frac{1}{3}$
   3. $\frac{1}{6}$
   4. $\frac{2}{3}$
2. What is the theoretical probability of flipping a coin and getting tails?
   1. 1
   2. $\frac{1}{4}$
   3. $\frac{1}{3}$
   4. $\frac{1}{2}$
3. What is the probability of rolling a 2 on a die and flipping a coin and getting heads?
   1. $\frac{1}{12}$
   2. $\frac{1}{2}$
   3. $\frac{1}{6}$
   4. $\frac{1}{8}$
4. What is the probability of rolling an even number on a fair 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 number greater than 4 on a fair six-sided die?
   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$
6. If you flip a coin twice, what is the probability of getting heads both times?
   1. $\frac{1}{2}$
   2. $\frac{1}{3}$
   3. $\frac{1}{4}$
   4. $\frac{3}{4}$
7. What is the probability of rolling a 1 or a 6 on a fair six-sided die?
   1. $\frac{1}{2}$
   2. $\frac{1}{3}$
   3. $\frac{1}{6}$
   4. $\frac{2}{3}$