Theoretical probability
Master Theoretical probability in Grade 10 math. For equally likely outcomes, the theoretical probability of an event is the ratio: $P(\text{event}) .
Key Concepts
For equally likely outcomes, the theoretical probability $P$ of an event is the ratio: $$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$.
Example 1: $P(\text{rolling a number 4 on a 6 sided die}) = \frac{2 \text{ (5, 6)}}{6 \text{ (1, 2, 3, 4, 5, 6)}} = \frac{1}{3}$.
Example 2: A random integer from 1 to 100 is chosen. $P(\text{multiple of 25}) = \frac{4 \text{ (25, 50, 75, 100)}}{100} = \frac{1}{25}$.
Common Questions
What is Theoretical probability?
For equally likely outcomes, the theoretical probability of an event is the ratio: . Common mistake tip: A common mistake is to write the ratio of 'favorable' to 'unfavorable' outcomes (like 5 blue vs. 5 non-blue). Always remember the bottom number (the denominator) must be the total of all...
How do you apply Theoretical probability in practice?
Example 1: . Example 2: A random integer from 1 to 100 is chosen. . Example 3: .
Why is Theoretical probability important for Grade 10 students?
Theoretical probability is like making a super educated guess about what should happen in a perfect world. Think of it as the 'on-paper' chance of an event occurring, based on all the possibilities. It follows a simple, powerful formula: . Common mistake tip: A common slip-up is miscounting the...