In this Grade 8 lesson from Saxon Math Course 3, Chapter 7, students learn how to conduct a probability simulation using a spinner to model real-world events with a known theoretical probability. Students distinguish between theoretical probability and experimental probability by running multiple trials, recording outcomes, and calculating results such as the likelihood of winning at least once in three attempts. The lesson also challenges students to evaluate alternative simulation tools — including number cubes, coins, and colored marbles — to deepen their understanding of how to model a one-in-three probability.
Section 1
📘 Probability Simulation
A probability simulation is a method used to model random events. It helps estimate probabilities for situations that are too difficult or impractical to test directly.
This lesson is your hands-on introduction. You will soon build your own spinner, conduct trials, and analyze the results to find an experimental probability.
Section 2
Probability Simulation
A probability simulation is a method used to model random events, which helps in estimating probabilities when they are difficult to calculate theoretically or test experimentally.
Use a spinner with a “Win” section to simulate a chance of getting a cereal box prize.
To simulate a basketball player who makes 4 in 6 free throws, roll a die. Let numbers 1-4 be a “make” and 5-6 be a “miss”.
To simulate picking one pair of socks from 2 blue and 4 black socks, put 2 blue and 4 black tiles in a bag and draw two without looking.
Why buy 100 cereal boxes to find a prize? A simulation lets you “buy” them with a spinner or dice! It's a quick, cheap way to estimate the odds of winning without spending all your allowance on breakfast. It's like a math magic trick!
Section 3
Theoretical probability
Theoretical probability is what we expect to happen in theory. It is calculated as , assuming a world of perfect fairness.
The theoretical probability of a fair coin landing on heads is .
The theoretical probability of rolling a 5 on a standard six-sided die is .
The company claims 1 in 3 boxes win, so the theoretical probability of winning is .
Think of this as the “on paper” probability, what math predicts should happen. It’s like the game's official rulebook telling you the odds before you play. It’s the ideal chance, but remember, real life doesn't always follow the script perfectly!
Section 4
Calculating Experimental Probability
Experimental probability is based on the actual results of an experiment. It is calculated as
This is probability in the wild! It’s the result you get from actually doing an experiment, like your spinner simulation. It’s what happened, not what should have happened. The more trials you do, the more reliable this result becomes.
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Section 1
📘 Probability Simulation
A probability simulation is a method used to model random events. It helps estimate probabilities for situations that are too difficult or impractical to test directly.
This lesson is your hands-on introduction. You will soon build your own spinner, conduct trials, and analyze the results to find an experimental probability.
Section 2
Probability Simulation
A probability simulation is a method used to model random events, which helps in estimating probabilities when they are difficult to calculate theoretically or test experimentally.
Use a spinner with a “Win” section to simulate a chance of getting a cereal box prize.
To simulate a basketball player who makes 4 in 6 free throws, roll a die. Let numbers 1-4 be a “make” and 5-6 be a “miss”.
To simulate picking one pair of socks from 2 blue and 4 black socks, put 2 blue and 4 black tiles in a bag and draw two without looking.
Why buy 100 cereal boxes to find a prize? A simulation lets you “buy” them with a spinner or dice! It's a quick, cheap way to estimate the odds of winning without spending all your allowance on breakfast. It's like a math magic trick!
Section 3
Theoretical probability
Theoretical probability is what we expect to happen in theory. It is calculated as , assuming a world of perfect fairness.
The theoretical probability of a fair coin landing on heads is .
The theoretical probability of rolling a 5 on a standard six-sided die is .
The company claims 1 in 3 boxes win, so the theoretical probability of winning is .
Think of this as the “on paper” probability, what math predicts should happen. It’s like the game's official rulebook telling you the odds before you play. It’s the ideal chance, but remember, real life doesn't always follow the script perfectly!
Section 4
Calculating Experimental Probability
Experimental probability is based on the actual results of an experiment. It is calculated as
This is probability in the wild! It’s the result you get from actually doing an experiment, like your spinner simulation. It’s what happened, not what should have happened. The more trials you do, the more reliable this result becomes.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter