Theoretical Probability Examples for Middle School

📚 Quick Study Guide

• 🎲 Probability: A number between 0 and 1 that expresses how likely an event is to occur.
• ➗ Theoretical Probability Formula: $P(event) = \frac{Number\ of\ favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
• 💯 Certain Event: Probability = 1 (or 100%).
• 🚫 Impossible Event: Probability = 0.
• ➕ Complementary Events: The probability that an event will NOT occur is 1 minus the probability that it will occur. $P(not\ A) = 1 - P(A)$
• 📈 Expressing Probability: Can be expressed as a fraction, decimal, or percentage.
• 🔮 Theoretical vs. Experimental: Theoretical probability is what *should* happen, while experimental probability is what *actually* happens after trials.

Practice Quiz

1. What is the theoretical probability of rolling a 4 on a standard six-sided die?
   1. A) 1/2
   2. B) 1/3
   3. C) 1/6
   4. D) 1/4
2. A bag contains 5 red marbles and 3 blue marbles. What is the probability of randomly selecting a red marble?
   1. A) 3/8
   2. B) 5/8
   3. C) 3/5
   4. D) 5/3
3. What is the probability of flipping a fair coin and getting heads?
   1. A) 1/4
   2. B) 2/3
   3. C) 1/2
   4. D) 1
4. A spinner has 8 equal sections, numbered 1 through 8. What is the probability of spinning an odd number?
   1. A) 1/8
   2. B) 1/4
   3. C) 1/2
   4. D) 3/4
5. What is the probability of picking a vowel from the word "PROBABILITY"?
   1. A) 2/11
   2. B) 3/11
   3. C) 4/11
   4. D) 5/11
6. If the probability of rain tomorrow is 30%, what is the probability that it will NOT rain tomorrow?
   1. A) 30%
   2. B) 50%
   3. C) 60%
   4. D) 70%
7. A jar contains 4 green candies, 5 yellow candies, and 1 blue candy. What is the probability of randomly selecting a yellow candy?
   1. A) 1/2
   2. B) 1/10
   3. C) 4/10
   4. D) 5/10