Exploring Dependent Probability Concepts

What are the colors and quantities of the marbles used in the casino game?

• 5 green marbles only

• 4 green and 1 orange marble

• 3 green and 2 orange marbles

• 2 green and 3 orange marbles

How much does it cost to play the marble game?

• $0.35

• $0.45

• $0.50

• $0.25

What is the probability of drawing a green marble first?

• 3/4

• 2/5

• 1/2

• 3/5

Why are the events of drawing marbles not considered independent?

• Because all marbles are the same color

• Because the outcome of the second draw depends on the first

• Because the color of the marbles affects the outcome

• Because the first marble is replaced

What is the probability of drawing a second green marble given the first one was green?

• 3/5

• 2/5

• 1/4

• 1/2

What effect does not replacing the first drawn marble have on the game?

• It decreases the total number of marbles in the bag

• It increases the cost of the game

• It makes the game easier

• It makes the second draw dependent on the first

What is the total probability of winning the game by drawing two green marbles?

• 60%

• 30%

• 25%

• 50%

What is the expected value of playing the game?

• $0.40

• $0.30

• $0.35

• $0.25

Is it economically sensible to play the game?

• No, because the expected value is lower than the cost

• No, because the game is rigged

• Yes, because the probability of winning is high

• Yes, because the expected value is higher than the cost

If the first drawn green marble was replaced, would the game be more appealing to play?

• Yes, because it increases the probability of winning

• Yes, because it makes the events independent

• No, because it does not change the cost of the game

• No, because the expected value remains the same