Experimental Probability with Dice

The video tutorial explains the difference between theoretical and experimental probability using dice as an example. It covers the concept of sample space and how to calculate probabilities for specific events, such as rolling a six or an even number. The tutorial then introduces experimental probability, highlighting how it differs from theoretical probability and demonstrating this through a practical example of rolling dice multiple times.

What is the main difference between theoretical and experimental probability?

• Theoretical probability is always more accurate than experimental probability.

• Theoretical probability is based on actual experiments, while experimental probability is based on ideal conditions.

• Theoretical probability is calculated using known outcomes, while experimental probability is based on actual experiments.

• Theoretical probability changes with each experiment, while experimental probability remains constant.

In the context of dice, what does the term 'sample space' refer to?

• The number of times a die is rolled.

• The total number of possible outcomes when rolling a die.

• The number of favorable outcomes when rolling a die.

• The probability of rolling a six.

How is the probability of rolling a six on a fair die calculated?

• 1/4

• 1/6

• 1/3

• 1/2

What is meant by 'favorable outcomes' in probability?

• The outcomes that are most likely to occur.

• The outcomes that are least likely to occur.

• The outcomes that are of interest in a probability experiment.

• The total number of possible outcomes.

If you want to find the probability of rolling an even number on a die, what is the probability?

• 1/6

• 1/4

• 1/2

• 1/3

What does experimental probability rely on?

• Actual experimental results

• Assumptions about fairness

• Predictions based on past data

• Theoretical calculations

Why might experimental probability differ from theoretical probability?

• Because theoretical probability is based on assumptions.

• Because experimental probability is based on actual results which can vary.

• Because theoretical probability changes with each experiment.

• Because experiments are always perfect.

What happens to experimental probability as the number of trials increases?

• It becomes more unpredictable.

• It remains constant.

• It approaches the theoretical probability.

• It becomes less accurate.

In a practical demonstration, if you roll a die three times and get a six once, what is the experimental probability of rolling a six?

• 1/2

• 1/6

• 1/3

• 1/4

What is the expected outcome if you roll a fair die many times?

• The experimental probability will never stabilize.

• The experimental probability will be exactly 1/3.

• The experimental probability will approach the theoretical probability of 1/6.

• The experimental probability will always be 1/6.