Exploring Theoretical vs Experimental Probability with Spinners

This video tutorial explains the difference between theoretical and experimental probability using spinners as an example. Theoretical probability is calculated mathematically, while experimental probability is determined through actual experiments. The video demonstrates how to use a calculator simulator to conduct probability experiments with spinners, showing how results can vary from theoretical expectations. Over many trials, experimental results should align more closely with theoretical predictions.

What is the main difference between theoretical and experimental probabilities?

• Theoretical is based on experiments, while experimental is based on calculations.

• Theoretical and experimental probabilities are essentially the same.

• Theoretical is derived from mathematical calculations, while experimental is based on actual outcomes.

• Theoretical is less accurate than experimental.

What is the purpose of spinning a spinner multiple times in an experiment?

• To test the durability of the spinner

• To ensure the spinner is balanced

• To determine the experimental probability of landing on each section

• To practice spinning techniques

If a spinner is divided into four equal sections, what is the theoretical probability of it landing on any one section?

• 0.25

• 1

• 0.5

• 0.75

What does the theoretical probability of 0.25 signify in the context of a four-section spinner?

• Each section is 25% larger than the others

• The spinner will always stop on one section

• Each section has a 25% chance of being landed on

• The spinner is 25% likely to be biased

How do you access the probability simulation app on a calculator?

• It is not available on calculators

• Download it from the internet

• Go to settings and select 'Prob Sim'

• Click on apps and select 'Prob Sim'

How can you view the results of a spinner simulation in table form on a calculator?

• Download the results to a computer

• Press the 'table' button under the graph display

• There is no option to view in table form

• Calculate manually from the graph

In an experiment spinning the spinner 10 times, what was the experimental probability of landing on section 2?

• 0.8

• 0.4

• 0.6

• 0.2

What should happen to the experimental probability if the number of trials increases?

• It becomes less reliable

• It should converge to the theoretical probability

• It remains constant regardless of trials

• It should diverge from the theoretical probability

What does an experimental probability of 0.4 for landing on section 2 indicate about the experiment?

• The theoretical probability is incorrect

• In 40% of spins, the spinner landed on section 2

• The spinner is biased towards section 2

• Section 2 is larger than the others

Why is it important that theoretical and experimental probabilities converge with more trials?

• Both A and B

• It confirms the mathematical calculations are correct

• Neither A nor B

• It shows the experiment is conducted properly