Summary of "1.1 Experimental Probability"

Main Ideas and Concepts

Definition of Probability
Probability is the likelihood of an Event occurring. An "Outcome" is a possible result of an experiment.
Experimental Probability
Defined by the formula:

P(A) = n(A) / n(T)

Where:
- P(A) = Probability of Event A
- n(A) = Number of times Event A occurs
- n(T) = Total number of trials
Experimental Probability is based on actual trials or experiments, such as rolling a die or spinning a spinner.
Example Calculation
A spinner produces results:
- Orange: 8 times
- Red: 4 times
- Purple: 8 times
- Green: 12 times
Total trials: 32

Calculating probabilities for each color:
- Orange: 8/32 = 0.25 = 25%
- Purple: 8/32 = 0.25 = 25%
- Red: 4/32 = 0.125 = 12.5%
- Green: 12/32 = 0.375 = 37.5%
Sum of Probabilities
The sum of all probabilities for a Probability experiment must equal 1 (or 100%).
Subjective Probability
Based on intuition rather than mathematical calculations. Examples include predicting outcomes based on gut feelings. Ranges from 0 (impossible) to 1 (certain).
Practical Examples
Scenarios are provided to illustrate subjective Probability:
- The sun setting in the west is certain (1).
- The next person entering the cafeteria is likely a student (high Probability).
- The Toronto Maple Leafs winning a Stanley Cup is unlikely (low Probability).
Conclusion
Experimental Probability helps in making predictions based on trials. Understanding basic Probability concepts is essential for further studies.