Theoretical Probability
Theoretical probability is the probability of an event calculated based on the possible outcomes, assuming all outcomes are equally likely. It is often expressed as a fraction, decimal, or percentage.
Example:
- Rolling a die: The theoretical probability of rolling a 6 is 1/6, as there are six possible outcomes (numbers 1 to 6), and only one outcome is a 6.
Experimental Probability
Experimental probability is the probability of an event based on the results of an experiment or observation. It is calculated by dividing the number of times the event occurs by the total number of trials.
Example:
- Tossing a coin: If you toss a coin 10 times and get heads 6 times, the experimental probability of getting heads is 6/10 or 60%.
Key Differences
- Theoretical Probability: Calculated based on possible outcomes.
- Experimental Probability: Calculated based on actual results.
Relationship between Theoretical and Experimental Probability
- As the number of trials in an experiment increases, the experimental probability tends to get closer to the theoretical probability.
Practical Insights
- Theoretical probability helps us predict the likelihood of an event happening, while experimental probability helps us understand the actual frequency of an event in real-world scenarios.
- Both theoretical and experimental probabilities are important tools in various fields like statistics, gambling, and decision-making.
