Experimental probability
Experimental probability is the probability determined by actually performing an experiment and recording results, calculated as the number of favorable outcomes divided by the total number of trials. If you flip a coin 50 times and get heads 23 times, the experimental probability of heads is 23/50 = 0.46 = 46%. This Grade 7 math skill from Saxon Math, Course 2 distinguishes between theoretical probability (what should happen based on math) and experimental probability (what actually happens based on data), building critical thinking about variability and the law of large numbers.
Key Concepts
Property $$ \text{Experimental probability} = \frac{\text{number of favorable outcomes}}{\text{number of trials}} $$.
Examples A player made 60 free throws in 80 attempts. Her experimental probability of making a shot is $\frac{60}{80} = \frac{3}{4}$. A spinner landed on blue 50 times out of 200 spins. The experimental probability is $\frac{50}{200} = \frac{1}{4}$.
Explanation Forget theory—this is about what actually happens when you run an experiment. It's like finding a basketball player's free throw percentage by looking at their real game stats, not just guessing what should happen. It is probability based on real world data from repeated trials.
Common Questions
What is experimental probability?
Experimental probability is calculated from actual trial data: P(event) = number of favorable outcomes divided by number of trials. It reflects what actually happened in the experiment, which may differ from the theoretical value.
How is experimental probability different from theoretical probability?
Theoretical probability is based on mathematical reasoning about equally likely outcomes (like P(heads) = 1/2 for a fair coin). Experimental probability comes from actually conducting the experiment and recording results.
Why might experimental probability differ from theoretical probability?
Real experiments involve chance variation. Flipping a coin 10 times might give 7 heads, not exactly 5. As the number of trials increases, experimental probability tends to approach the theoretical value.
How many trials do you need for experimental probability to be reliable?
More trials generally give more reliable estimates. With 10 trials, results can vary widely. With 1,000 trials, the experimental probability is usually very close to the theoretical probability.
When do students learn experimental probability?
Experimental probability is introduced in Grade 7 alongside theoretical probability. Saxon Math, Course 2 covers it in Chapter 10.
What are common mistakes with experimental probability?
Students sometimes confuse the number of favorable outcomes with the fraction of total outcomes, or miscount trials. Always divide favorable outcomes by total trials, not by some other count.
How does experimental probability connect to real-world statistics?
Medical trials, quality control testing, and polling all use experimental probability. A vaccine's 90% efficacy means 90% of trials showed favorable outcomes — that is experimental probability at work.