Use this formula to find our experimental probability. Make sure the numerator is what we are looking for!
The Great Carnival Challenge: Simple vs. Compound
At the carnival, there are two games you can play.Your job is to use experimental probability to decide which carnival game gives players the better chance of winning.[br][br][b]The first game is a simple event[/b] because there is only one condition to win. Players spin the roulette wheel once and win [u][color=#ff0000]if it lands on red.[/color][/u][br][br][b]The second game is a compound event[/b] because there are two conditions needed to win. Players spin the roulette wheel and win only [u][color=#ff0000]if the wheel lands on a red and even number.[/color][/u]
Carnival Game
Winning Prediction
Which carnival game do you think gives players a better chance of winning? Why?
Theoretical Probability Of Simple Event
What is the theoretical probability of landing on red?
Theoretical Probability Of Compound Event
What is the theoretical probability of landing on red AND an even number?
Conducting Our Experiment
Now let’s test our predictions by conducting an experiment using the roulette wheel. [br][br]First, complete the [u]simple event[/u] by [b]spinning the roulette wheel 10 times[/b] and recording how many times the wheel lands on red. Use the recording sheet linked below to keep track of your trials and results.[br][br]Next, complete the [u]compound event[/u] by [b]spinning the roulette wheel 10 times[/b] and recording how many times the wheel lands on a red AND an even number. Use the recording sheet linked below to keep track of your trials and results.[br][br]Link to Recording Sheet: [url=https://utrgv-my.sharepoint.com/:w:/g/personal/olivia_gonzalez02_utrgv_edu/IQDtCknIT5HDSoPKaZ4Qw4fFAXzhTgAmW-4yoElN2cPPKrU?e=ZoKi5x]Experimental Recording Sheet[/url][br][br]After completing both experiments, use your data to create the experimental probability for each event using the formula shown below.
Carnival Game Trial
Simple Event Questions
[b]Answer these questions below using the simulation.[/b]
Experimental Relation To Theoretical Prediction Simple Event
Before you do your experiment, do you predict your experimental probability will match the theoretical probability exactly? Why or why not?
10 Trial Experiment Simple Event
After [b]spinning the roulette wheel 10 times[/b] and recording how many times[b] the wheel landed on red[/b], what was your experimental probability? (Keep in mind that yours might look different from your peers)
Analyze Simple Event
Did you notice any patterns or events happening more often during your trials? If so, what patterns did you observe?
Compare Experimental and Theoretical Probability Simple Event
How close was your experimental probability to the theoretical probability? Do you think we need to do more trials?
Compound Event Questions
[b]Answer these questions below using the simulation.[/b]
Experimental Relation To Theoretical Prediction Compound Event
Before you do your experiment, do you predict your experimental probability will match the theoretical probability exactly? Why or why not?
10 Trial Experiment Compound Event
After [b]spinning the roulette wheel 10 times[/b] and recording how many times[b] the wheel landed on red AND an even number[/b], what was your experimental probability? (Keep in mind that yours might look different from your peers)
Analyze Compound Event
Did you notice any patterns or events happening more often during your trials? If so, what patterns did you observe?
Compare Experimental and Theoretical Probability Compound Event
How close was your experimental probability to the theoretical probability? Do you think we need to do more trials?
The Law of Large Numbers
[b]The Law of Large Numbers states that as the number of trials increases, the experimental probability gets closer to the theoretical probability. [/b]
More Trials
Do you think that if we completed more trials, our experimental probability would become closer to the theoretical probability? Why?
More Trials Experiment
Now let’s test the Law of Large Numbers by increasing our number of trials. Keep the 10 trials you already completed and perform 10 more trials to make a total of 20 trials. [br][br]Use the same recording sheet to continue tracking your results for both the simple event and the compound event. [br][br]After completing the additional trials, calculate the new experimental probability and compare it to the theoretical probability.
Carnival Game Trial
Simple Event Questions
[b]Answer these questions below using the simulation.[/b]
20 Trial Experiment Simple Event
After [b]spinning the roulette wheel 20 times[/b] and recording how many times[b] the wheel landed on red[/b], what was your experimental probability? (Keep in mind that yours might look different from your peers)
Analyze Simple Event
Did you notice any patterns or events happening more often during your trials? If so, what patterns did you observe?
Compare Experimental and Theoretical Probability Simple Event
Was your experimental probability closer to the theoretical probability?
Compound Event Questions
[b]Answer these questions below using the simulation.[/b]
20 Trial Experiment Compound Event
After [b]spinning the roulette wheel 20 times[/b] and recording how many times[b] the wheel landed on red AND an even number[/b], what was your experimental probability? (Keep in mind that yours might look different from your peers)
Analyze Compound Event
Did you notice any patterns or events happening more often during your trials? If so, what patterns did you observe?
Compare Experimental and Theoretical Probability Compound Event
Was your experimental probability closer to the theoretical probability?
The Great Carnival Challenge
Now let’s use everything we have calculated to decide which carnival game gives other players and me the better chance of winning. [br][br]Think about your theoretical probability, experimental probability, and the results from your trials before answering the final question.
Which Game Should I Play?
Based on your experimental probability data, [b][u]which carnival game gives players the better chance of winning[/u][/b]? Use evidence from your trials to justify your answer.
Great Job, Class! Thank you for participating and helping me find what game to play to win a prize.
