Empirical and Calculated Probability Concepts

The video tutorial introduces empirical probability, explaining it as an estimated probability based on past evidence or experimental results. It contrasts empirical probability with theoretical probability, which is calculated from a defined sample space. The tutorial uses examples like a baseball player's batting average to illustrate empirical probability and explains calculated probability with the example of drawing an ace from a deck of cards. It also covers the concept of expected value using empirical probability and concludes by summarizing the differences between empirical and calculated probabilities.

What is empirical probability based on?

• Past evidence or experimental results

• Theoretical assumptions

• Future predictions

• Random guesses

How does empirical probability differ from theoretical probability?

• Empirical probability requires no data, while theoretical requires experiments.

• Empirical probability is based on past data, while theoretical is based on a defined sample space.

• Empirical probability is exact, while theoretical is an estimate.

• Empirical probability is always higher than theoretical probability.

What is an example of empirical probability in sports?

• The number of home runs

• The team's win-loss record

• The number of games played

• A player's batting average

How is a player's batting average calculated?

• Total number of at-bats divided by total number of hits

• Total number of home runs divided by total number of games

• Total number of hits divided by total number of at-bats

• Total number of games played divided by total number of hits

What is the probability of drawing an ace from a standard deck of cards?

• 1/13

• 1/4

• 1/52

• 4/52

What distinguishes calculated probability from empirical probability?

• Calculated probability requires experiments.

• Calculated probability is always an estimate.

• Calculated probability is based on past events.

• Calculated probability is exact and does not require prior experiments.

In the business example, what is the empirical probability of a customer choosing product Y?

• 25%

• 35%

• 45%

• 50%

How many units of product Y are expected to be sold based on empirical probability?

• 2,000

• 2,450

• 3,000

• 3,500

What is the main difference between empirical and calculated probability?

• Empirical probability is exact, calculated is an estimate.

• Empirical probability is based on past data, calculated is exact without experiments.

• Empirical probability requires no data, calculated requires past data.

• Empirical probability is always higher than calculated probability.