Lesson 59: Experimental Probability

New Concept

Experimental probability is determined by data from an experiment. It is the ratio of the number of times an event occurs to the number of trials.

What’s next

You’re just getting started. Next, we’ll use this formula in worked examples and learn how to simulate experiments to find probabilities on your own.

Property

Experimental probability is the ratio of the number of times an event occurs to the number of trials.

Examples

A basketball player makes 85 free throws in 100 attempts. The experimental probability of making a shot is $\frac{85}{100}$ or $\frac{17}{20}$.
Since she added a veggie burger to the menu, 40 out of 160 customers have ordered it. The probability that the next customer will order one is $\frac{40}{160}$ or $\frac{1}{4}$.
If a YouTuber gets 100 likes on a video with 1000 views, the probability that a viewer will like a video is $\frac{100}{1000}$ or $0.1$.

Explanation

Think of this as probability in the real world! It’s not about what should happen, but what actually happened when you tried it. Like a batting average, it’s based on past performance, not just theory.

Property

Theoretical probability is found by analyzing a situation, while experimental probability is determined by data from trials. As the number of trials increases, the experimental probability tends to get closer to the theoretical probability.

Examples

The theoretical probability of rolling a 4 on a six-sided die is $\frac{1}{6}$.
If you roll a die 30 times and get a '4' six times, the experimental probability is $\frac{6}{30}$, or $\frac{1}{5}$.
After 600 rolls, your experimental probability might be $\frac{98}{600}$, which is much closer to the theoretical $\frac{1}{6}$.

Explanation

Theory is what a perfect world predicts, like a 50% chance for heads on a coin flip. Experiments are what really happen—you might get 4 heads in 10 flips. The more you flip, the closer reality gets to theory!

Property

An experiment can be simulated using tools like spinners, number cubes, or drawing marbles from a bag. This is useful when conducting a real experiment is impractical or would take too long.

Examples

• To simulate a 25% chance of rain, you can draw from a bag with 1 red marble (rain) and 3 blue marbles (no rain).
• To simulate a batter with a .500 average (a $\frac{1}{2}$ chance of a hit), you can just flip a coin for each at-bat.
• To simulate a $\frac{2}{3}$ probability of a bus arriving on time, you could roll a die, letting numbers 1-4 be 'on time' and 5-6 be 'late'.

Explanation

Why wait weeks to see if your favorite flight is on time? You can fake it! Use a spinner or dice to mimic the chances and run dozens of 'trials' in minutes to get a quick prediction.