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Experimental Probability

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Experimental Probability

Study Guide

Key Definition

Experimental probability is the ratio of the number of favorable outcomes to the total number of trials: $\frac{\text{number of favorable outcomes}}{\text{total number of trials}}$

Important Notes

Theoretical probability assumes all outcomes are equally likely.
Experimental probability is based on actual experiments or trials.
As the number of trials increases, experimental probability approaches theoretical probability.
You can use experimental probability when the theoretical probability is unknown.
Examples include flipping a coin or rolling a die multiple times.

Mathematical Notation

$\frac{n(A)}{N}$ represents experimental probability (event A occurred n(A) times in N trials)

$P(A)$ denotes the probability of event A

$n(A)$ is the number of times event A occurred

$N$ is the total number of trials

Use P(A)=n(A)/N to express experimental probability

Why It Works

Experimental probability provides a practical estimate of likelihood by using $\text{actual data}$ from experiments. This approach is foundational for developing a probability distribution from empirical data.

Remember

Experimental probability formula: $\frac{\text{number of favorable outcomes}}{\text{total number of trials}}$

Quick Reference

Experimental Probability:$\frac{\text{favorable outcomes}}{\text{total trials}}$

Understanding Experimental Probability

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Video explanation of this concept

Beginner

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Beginner Explanation

Experimental probability is calculated by dividing observed favorable outcomes by the total number of trials. For example, if you flip a coin 10 times and get 7 heads, the experimental probability of heads is $\frac{7}{10}$.

Practice Problems

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Quick Quiz

Single Choice Quiz

Beginner

If you flip a coin 10 times and get 7 heads, what is the experimental probability of getting heads?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You draw a marble from a bag with replacement 100 times and record each color. After 100 draws, you have 20 blue marbles, 30 red, and 50 green. What is the experimental probability of drawing a blue marble?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

In a game, you roll a die 60 times and roll a 4 exactly 10 times. How does the experimental probability compare to the theoretical probability?

Challenge Quiz

Single Choice Quiz

Advanced

You conduct an experiment where you flip a coin 100 times and get 48 tails. What can you infer about the fairness of the coin?

Recap

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