theoretical probability Grade 7 examples

📚 Quick Study Guide

• 🎲 Definition: Theoretical probability is what we *expect* to happen in an ideal situation.
• 🔢 Formula: Theoretical Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
• 🪙 Example: Flipping a coin. There's 1 favorable outcome (heads) and 2 total possible outcomes (heads or tails). So, the probability of getting heads is $\frac{1}{2}$.
• 🎯 Key Point: Theoretical probability assumes all outcomes are equally likely.
• 📈 Range: Probability values are always between 0 and 1 (inclusive). 0 means impossible, and 1 means certain.

Practice Quiz

1. What is the theoretical probability of rolling a 4 on a standard six-sided die?
   1. $\frac{1}{2}$
   2. $\frac{1}{3}$
   3. $\frac{1}{6}$
   4. $\frac{2}{3}$
2. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the theoretical probability of picking a blue marble at random?
   1. $\frac{1}{2}$
   2. $\frac{3}{10}$
   3. $\frac{1}{5}$
   4. $\frac{2}{5}$
3. What is the probability of flipping a fair coin and getting tails?
   1. 1
   2. $\frac{1}{4}$
   3. $\frac{1}{2}$
   4. 0
4. A spinner has 8 equal sections labeled 1 to 8. What is the theoretical probability of spinning an odd number?
   1. $\frac{1}{8}$
   2. $\frac{1}{4}$
   3. $\frac{1}{2}$
   4. $\frac{3}{4}$
5. What is the probability of drawing a heart from a standard deck of 52 cards?
   1. $\frac{1}{2}$
   2. $\frac{1}{4}$
   3. $\frac{1}{13}$
   4. $\frac{3}{52}$
6. A jar contains 4 purple candies, 6 yellow candies and 2 orange candies. If you pick one candy without looking, what is the theoretical probability you'll pick a purple candy?
   1. $\frac{1}{2}$
   2. $\frac{1}{3}$
   3. $\frac{1}{6}$
   4. $\frac{1}{4}$
7. What is the probability of rolling either a 1 or a 6 on a standard six-sided die?
   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$