Mathematics
Grade 9
15 min
Experimental probability
Experimental probability
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define experimental probability and distinguish it from theoretical probability.
Calculate the experimental probability of an event using data from an experiment.
Design and conduct a simple probability experiment to gather data.
Use experimental probability to make predictions about future events.
Explain the relationship between the number of trials and the accuracy of experimental probability (the Law of Large Numbers).
Analyze and interpret the results of a probability experiment presented in tables or charts.
Ever wonder why a basketball player's free-throw percentage is 75%? It's not a guess, it's based on what they've actually done in games! 🏀
This tutorial will explore experimental probability, which is the probability of an...
2
Key Concepts & Vocabulary
TermDefinitionExample
ExperimentAn action or process with an observable result that cannot be known in advance.Rolling a six-sided die.
TrialA single performance of an experiment.One roll of the die.
OutcomeA possible result of a single trial.The die lands on the number 4.
EventA specific outcome or a collection of outcomes that we are interested in.The event of rolling an even number (outcomes 2, 4, or 6).
FrequencyThe number of times a specific event occurs in an experiment.In 50 rolls of a die, the number 4 appeared 9 times. The frequency of rolling a 4 is 9.
Experimental ProbabilityA probability calculated from the results of an experiment. It is the ratio of the frequency of an event to the total number of trials.If you flip a coin 20 times and get 12 heads, the experimental probabil...
3
Core Formulas
Experimental Probability Formula
P(\text{Event}) = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}
Use this formula to calculate the probability of an event based on data you have collected from an experiment. The result can be expressed as a fraction, decimal, or percentage.
The Law of Large Numbers
As the number of trials in an experiment increases, the experimental probability will tend to get closer to the theoretical probability.
This is a concept, not a calculation formula. It means that results from a small number of trials can be misleading, but results from a very large number of trials are usually a good estimate of the true probability.
Prediction Formula
\text{Predicted Frequency} = P(\text{Event}) \times \text{Number of future...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A factory's quality control shows that the experimental probability of a microchip being defective is 0.5%. The factory produces 20,000 microchips each day. Based on this data, what is the predicted number of *non-defective* microchips produced over a 5-day work week?
A.100
B.500
C.99,000
D.99,500
Challenging
A student wants to determine the experimental probability that a thumbtack, when dropped, will land point up. Which of the following experimental designs is most likely to produce a reliable result?
A.Dropping 10 thumbtacks from a height of 10 cm onto a carpeted floor.
B.Dropping one thumbtack 500 times from a consistent height of 30 cm onto a hard, flat surface.
C.Dropping 500 thumbtacks all at once from a bag onto a variety of different surfaces.
D.Dropping one thumbtack 10 times from various heights onto a soft towel.
Challenging
A survey of 300 Grade 9 students about their favorite subject was conducted. 30% chose Math, 95 students chose Science, and the rest chose either English or History. If the experimental probability of a student choosing History was 1/4, how many students chose English?
A.90
B.75
C.300
D.45
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free