Mathematics
Grade 8
15 min
Make predictions
Make predictions
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1
Introduction & Learning Objectives
Learning Objectives
Define and differentiate between theoretical and experimental probability.
Calculate the theoretical probability of an event.
Calculate the experimental probability of an event based on observed data.
Use both theoretical and experimental probabilities to make predictions about future events.
Understand that predictions are estimates and not guarantees.
Apply probability predictions to solve real-world problems.
Ever wonder if it will rain tomorrow? 🌧️ Or how many times you'll roll a '6' in a game? Probability helps us make educated guesses about what might happen!
In this lesson, you'll learn how to use the power of probability to make predictions about future events. This skill is crucial for understanding and anticipating outcomes...
2
Key Concepts & Vocabulary
TermDefinitionExample
ProbabilityA measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1 (or 0% and 100%).The probability of flipping a coin and getting heads is 1/2 or 50%.
OutcomeA possible result of an experiment or situation.When rolling a standard six-sided die, the outcomes are 1, 2, 3, 4, 5, or 6.
EventA specific outcome or a set of outcomes that you are interested in.When rolling a die, getting an 'even number' (2, 4, or 6) is an event.
Theoretical ProbabilityThe probability of an event based on mathematical reasoning and the possible outcomes, assuming all outcomes are equally likely. It's what *should* happen.The theoretical probability of rolling a '4' on a fair six-sided die is 1/6.
Experimental ProbabilityThe...
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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 formula to calculate the probability of an event when you know all possible outcomes and assume they are equally likely. This tells you what *should* happen.
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 collected from actual experiments or observations. This tells you what *did* happen.
Making Predictions Formula
$\text{Predicted occurrences} = P(\text{event}) \times \text{Total number of trials}$
Once you have a probability (either theoretical or experimental), use th...
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Challenging
A fair coin has landed on heads 6 times in a row. Which statement best describes the prediction for the next 100 flips?
A.Tails is now more likely to occur, so the prediction for heads should be less than 50.
B.The coin is 'hot' on heads, so the prediction for heads should be more than 50.
C.Each flip is an independent event, so the theoretical probability of heads is still 1/2, and the best prediction is 50 heads.
D.The experimental probability from the first 6 flips (100% heads) should be used, predicting 100 heads.
Challenging
A student suspects a six-sided die is biased. She rolls it 20 times and gets a '6' eight times. A friend tells her to predict the number of 6s in the next 1,000 rolls. Which is the most reasonable approach?
A.Use the theoretical probability (1/6), because a die must be fair. The prediction would be about 167.
B.Use the experimental probability (8/20), because the initial data suggests a bias. The prediction would be 400.
C.Ignore the data and assume 0, because you can't predict the future.
D.Use the experimental probability (8/20), but state that the prediction is highly uncertain due to the small initial sample size.
Challenging
A carnival game costs $3 to play. The theoretical probability of winning is 1/10. The prize for winning is $20. If 500 people play the game, what is the carnival's predicted net profit?
A.$500
B.$1,000
C.$1,500
D.$2,000
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