Mathematics
Grade 8
15 min
Experimental probability
Experimental probability
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Introduction & Learning Objectives
Learning Objectives
Define experimental probability and distinguish it from theoretical probability.
Identify the number of favorable outcomes and the total number of trials in an experiment.
Calculate the experimental probability of an event as a ratio.
Express experimental probability as a fraction, decimal, or percentage.
Interpret experimental probability in real-world contexts.
Compare experimental probability to theoretical probability and explain potential differences.
Ever wonder why a weather forecast says there's a 70% chance of rain? ☔️ It's not just a guess; it's often based on what happened in the past!
In this lesson, you'll discover how to predict the likelihood of events by actually performing experiments and observing the results. This...
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Key Concepts & Vocabulary
TermDefinitionExample
Experimental ProbabilityThe probability of an event occurring based on the results of an experiment or observation. It's what *actually* happens when you perform trials.If you flip a coin 10 times and get heads 6 times, the experimental probability of getting heads is 6/10.
TrialA single performance of an experiment or observation.Each time you flip a coin, that's one trial. Each time you spin a spinner, that's one trial.
OutcomeA possible result of a single trial.When flipping a coin, the possible outcomes are 'heads' or 'tails'.
EventA specific outcome or a set of outcomes that you are interested in.Getting 'heads' when flipping a coin is an event. Rolling an even number on a die is an event.
Favorable OutcomeAn outcome...
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Core Formulas
Formula for Experimental Probability
$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}$
Use this formula to calculate the probability of an event based on observed results from an experiment. The result is usually expressed as a fraction, decimal, or percentage.
Law of Large Numbers (Relationship to Theoretical Probability)
As the number of trials in an experiment increases, the experimental probability of an event generally gets closer to its theoretical probability.
This rule helps us understand why experimental results might differ from theoretical predictions, especially with a small number of trials. More trials lead to more reliable experimental probabilities.
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Challenging
Two friends track the number of bicyclists wearing helmets. Amy sees 80 bicyclists, and 60 of them are wearing helmets. Ben sees 120 bicyclists, and 90 are wearing helmets. If they combine their data, what is the new experimental probability that a bicyclist is wearing a helmet?
A.150/200
B.75/100
C.60/80 + 90/120
D.75%
Challenging
A student flips a coin 4 times and gets Tails every time. They conclude, 'The experimental probability of getting Tails is 100%, so I am guaranteed to get Tails on the next flip.' What is the primary flaw in this reasoning?
A.The calculation is wrong; the probability is 1/4.
B.The conclusion is based on the Law of Large Numbers.
C.The conclusion confuses experimental probability from a very small sample with the theoretical probability of a future independent event.
D.The coin is definitely unfair.
Challenging
A quality inspector tests two different components of a toy car: wheels and paint. Out of 400 cars, 12 have faulty wheels and 20 have a bad paint job. No car has both faults. What is the experimental probability that a randomly selected car has a fault with either its wheels OR its paint?
A.32/400
B.8/400
C.1/400
D.20/400
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