Mathematics
Grade 7
15 min
Make predictions
Make predictions
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1
Introduction & Learning Objectives
Learning Objectives
Define theoretical and experimental probability.
Calculate theoretical probability for simple events.
Calculate experimental probability from observed data.
Use probability to make predictions about future events.
Compare theoretical and experimental probabilities.
Understand how sample size can affect the accuracy of predictions.
Apply probability predictions to solve real-world problems.
Ever wonder if it will rain tomorrow 🌧️, or if your favorite team will win the next game 🏆? We make predictions all the time!
In this lesson, you'll learn how to use the power of probability to make informed predictions about future events. Understanding how to make predictions helps us make better decisions and understand the likelihood of things happening in...
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Key Concepts & Vocabulary
TermDefinitionExample
ProbabilityThe measure of how likely an event is to occur. It's a number between 0 (impossible) and 1 (certain).The probability of flipping a coin and getting heads is 1/2 or 0.5.
OutcomeA possible result of an experiment or situation.When rolling a standard die, the outcomes are 1, 2, 3, 4, 5, or 6.
EventA specific outcome or a set of outcomes that you are interested in.Rolling an even number on a die is an event, which includes the outcomes 2, 4, and 6.
Theoretical ProbabilityThe probability of an event based on reasoning and what 'should' happen, assuming all outcomes are equally likely.The theoretical probability of picking a red card from a standard deck is 26/52 or 1/2.
Experimental ProbabilityThe probability of an event based on actual experimen...
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Core Formulas
Theoretical Probability Formula
$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
Use this when you know all possible outcomes and want to find the likelihood of a specific event occurring under ideal conditions.
Experimental Probability Formula
$P(\text{event}) = \frac{\text{Number of times the event occurred}}{\text{Total number of trials}}$
Use this when you have conducted an experiment or observed data, and you want to find the likelihood of an event based on those observations.
Making Predictions Formula
$\text{Predicted occurrences} = P(\text{event}) \times \text{Total number of future trials}$
Once you have a probability (either theoretical or experimental), multiply it by the total number of future trials...
5 more steps in this tutorial
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Challenging
A factory produces computer chips. A random sample of 500 chips is tested, and 4 are found to be defective. The factory produces 250,000 chips per month. However, the quality control manager wants the prediction to account for a margin of error and predicts between 1,800 and 2,200 defective chips. What is the prediction based solely on the sample data?
A.2,000
B.1,600
C.2,500
D.4,000
Challenging
A weather forecast states there is a 40% chance of rain for each of the next 5 days. A student concludes it is therefore guaranteed to rain on exactly 2 of those days (40% of 5 days = 2 days). Why is this conclusion incorrect?
A.The calculation is wrong; 40% of 5 is not 2.
B.The chance of rain is the same each day, so it must rain every day or not at all.
C.Probability predicts likelihood, not a definite outcome. Each day is an independent event.
D.40% chance of rain means it is more likely not to rain, so it will not rain at all.
Challenging
A city's animal shelter has 1,500 animals. A reporter takes a random sample of 60 animals and finds 24 dogs, 27 cats, and 9 other animals. The shelter manager claims that, based on their complete records, the theoretical probability of an animal being a dog is 1/2. Which is the better prediction for the number of dogs in the shelter?
A.prediction of 600 dogs, based on the reporter's experimental data.
B.prediction of 750 dogs, based on the manager's theoretical probability.
C.prediction of 24 dogs, because that is the number in the sample.
D.An average of the two predictions, which is 675 dogs.
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