Expected Value and Probability Concepts

The video tutorial explains a game involving a bag of marbles with different colors, each associated with a monetary outcome. It introduces the concept of expected value, which is the average gain or loss over many repetitions of the game. The tutorial details how to calculate the expected value by determining the probability of each outcome and multiplying it by the respective monetary gain or loss. The final expected value is calculated to be a loss of seventy-one cents, indicating that playing the game repeatedly would result in an average loss.

What are the possible outcomes when selecting a marble from the bag?

• Win $4, win $2, or lose $3

• Win $10, win $5, or lose $5

• Win $3, win $1, or lose $1

• Win $5, win $2, or lose $2

How is the expected value of a game defined?

• The minimum possible loss

• The maximum possible gain

• The average gain or loss over many plays

• The total gain from a single play

What is the probability of drawing a gold marble from the bag?

• 1/42

• 2/42

• 1/21

• 2/21

How many silver marbles are in the bag?

• 10

• 15

• 5

• 20

What is the probability of drawing a black marble?

• 15/42

• 20/42

• 25/42

• 30/42

Which operation is used to calculate the expected value?

• Division of total outcomes by probabilities

• Addition of probabilities

• Multiplication of outcomes by probabilities

• Subtraction of losses from gains

What is the expected value of the game in terms of dollars?

• -$0.71

• $0.00

• $0.71

• -$1.00

What does a negative expected value indicate in this game?

• A guaranteed win

• No change in value

• An average gain

• An average loss

How should the expected value be rounded?

• To the nearest ten cents

• To the nearest cent

• To the nearest five cents

• To the nearest dollar

Why is the negative sign not included when stating the average loss?

• Because it is already implied

• Because it is a gain

• Because it is a neutral value

• Because it is a rounding error