Experimental Probability

Learning Probability Through Hands-On Experiments and Real-World Data Analysis

CAPS Grade 10 Mathematical Literacy

Experimental probability (also called relative frequency) is the probability of an event occurring based on actual experimental results rather than theoretical reasoning. It is calculated by conducting experiments, collecting data, and analyzing the outcomes.

Key Concepts of Experimental Probability

What is Experimental Probability

Experimental probability is determined by performing an experiment and recording the outcomes. Unlike theoretical probability, which is based on reasoning, experimental probability uses actual data.

P(Event) = Number of times event occurs / Total number of trials

Law of Large Numbers

The Law of Large Numbers states that as the number of trials increases, the experimental probability gets closer to the theoretical probability.

Example: After 10 coin tosses, P(Heads)=0.7; after 1000 tosses, P(Heads)≈0.5

Experimental Probability Formula

Experimental P(Event) = Frequency of Event / Total Trials

Also known as Relative Frequency. This formula gives an empirical estimate of probability that becomes more reliable with more trials.

Example: If you flip a coin 50 times and get 28 heads, then P(Heads) = 28/50 = 0.56 = 56%

Expected Occurrences = Experimental Probability × Future Trials

Use experimental probability to make predictions about future outcomes.

Example: Based on P(Heads)=0.56, in 200 future tosses, expect about 0.56 × 200 = 112 heads.

The Experimental Process

1

Design Experiment

Plan a fair, repeatable experiment with clear procedures and random selection.

Design Elements: Clear procedure → Repeatable process → Random selection
2

Conduct Trials

Perform experiment multiple times, recording each outcome systematically.

Recording: Tally charts → Frequency tables → Consistent conditions
3

Collect & Organize Data

Create frequency tables showing how many times each outcome occurred.

Example: Heads: 47, Tails: 53 (100 trials)
4

Calculate Probability

Apply the experimental probability formula.

P(Heads) = 47/100 = 0.47 = 47%
5

Analyze & Interpret

Interpret results, compare with theory, discuss reliability.

Consider sample size and its effect on reliability

Game 1: Coin Toss Simulator

Test the Law of Large Numbers by tossing a virtual coin. The more tosses you do, the closer the experimental probability gets to 0.5!

Heads
0
Tails
0
Total
0
P(Heads)
0.000

Theoretical Probability: P(Heads) = 0.5 (50%)

Game 2: Dice Roll Simulator

Roll a fair die to see how experimental probability approaches 1/6 (≈0.1667) for each number as you increase rolls.

1
0
2
0
3
0
4
0
5
0
6
0
Total
0

Theoretical Probability: Each number = 1/6 ≈ 0.1667 (16.67%)

Game 3: Spinner Game

Spin a four-color spinner. Each color has a theoretical probability of 0.25 (25%). See how your experimental results compare!

Red
0
Blue
0
Green
0
Yellow
0
Total
0
SPIN

Theoretical Probability: Each color = 0.25 (25%)

Quiz 4: Test Your Knowledge

5 Questions
1 What is the formula for experimental probability
Successes × Trials
Successes / Trials
Trials / Successes
Successes + Trials
2 What does the Law of Large Numbers say
Small samples are more accurate
More trials = closer to theoretical probability
Probability is always 50%
Experimental probability never changes
3 After 200 coin tosses, you get 110 heads. P(Heads) is:
0.45
0.55
0.50
0.60
4 Another name for experimental probability is:
Theoretical probability
Relative frequency
Absolute probability
Fixed probability
5 Roll a die 60 times, get 8 sixes. P(6) is:
0.133
0.167
0.200
0.250
0/5

Game 5: Prediction Challenge

Based on the coin toss data, predict the next outcome. Test your understanding of probability and track your streak!

Real-World Applications

Insurance

Insurance companies use historical claim data (experimental probability) to calculate premiums and assess risk.

Quality Control

Manufacturers test samples to estimate defect rates and ensure product quality.

Weather Forecasting

"30% chance of rain" means that based on historical data, rain occurred in 30% of similar weather conditions.

Game Design

Game developers test probabilities to ensure fair and engaging gameplay mechanics.