A box contains two red balls, four green balls, and two white balls. You extract balls from the box with replacement 100 times. Eachh time you extract a red ball, you win $1; a green ball, you lose $0.50; a white ball, nothing happens.

-Make a box model of the net gain each time you play
-What is the expected value?
-By how much money will you be off the expected value?

I don't understand the box model part, but I drew a box with all the balls labeled with a color.
Then for expected value, I found the average: [$1(2)+$0.50(4)+$0(2)]/8 = 1/2. I know you plug it into the expected value equation but I'm notsure if the average is right.
I know to find how much money I will be off the expected value (aka find SD and SE).

I just need to know how to do the box model and if my average value is correct.

To create a box model, you represent each ball as a separate outcome in the box. You need to consider the probability of selecting each color of ball and the corresponding net gain/loss associated with it.

Here's the box model for this scenario:
- Red Ball: Win $1 with a probability of 2/8 = 1/4
- Green Ball: Lose $0.50 with a probability of 4/8 = 1/2
- White Ball: No gain/loss with a probability of 2/8 = 1/4

So the box model would look something like this:
- Red Ball: $1
- Red Ball: $1
- Green Ball: -$0.50
- Green Ball: -$0.50
- Green Ball: -$0.50
- Green Ball: -$0.50
- White Ball: $0
- White Ball: $0

Next, let's calculate the expected value:
Expected value = (Net gain/loss of each outcome) * (Probability of each outcome)
Expected value = ($1 * 1/4) + (-$0.50 * 1/2) + ($0 * 1/4)
Expected value = $0.25 - $0.25 + $0
Expected value = $0

So the expected value is $0, which means, on average, you can expect to neither gain nor lose money over multiple plays.

Since the expected value is $0, you won't be off the expected value by any amount.

To create a box model, you can visualize a box with compartments representing each type of ball. The number of compartments for each color of ball should reflect the respective number of balls in the box.

The box model for this scenario would have:
- 2 compartments labeled "Red" (for the two red balls)
- 4 compartments labeled "Green" (for the four green balls)
- 2 compartments labeled "White" (for the two white balls)

To determine the expected value, you need to calculate the weighted average of the possible outcomes based on their probabilities. In this case, the probabilities of drawing each type of ball are as follows:

- P(Red) = 2/8 = 1/4 (since there are two red balls out of eight balls in total)
- P(Green) = 4/8 = 1/2 (four green balls out of eight)
- P(White) = 2/8 = 1/4 (two white balls out of eight)

Now, assign the corresponding values to each outcome:
- Red: +$1 (winning $1)
- Green: -$0.50 (losing $0.50)
- White: $0 (nothing happens)

Calculate the expected value (EV) using the formula:

EV = (P(Red) * Value(Red)) + (P(Green) * Value(Green)) + (P(White) * Value(White))

= (1/4 * $1) + (1/2 * -$0.50) + (1/4 * $0)
= $0.25 - $0.25 + $0
= $0

The expected value, in this case, is $0.

To find how much money you will be off the expected value, you can calculate the standard deviation (SD) or the standard error (SE). However, for this specific scenario, you won't be off the expected value as the expected value is $0, which means you can expect to break even in the long run.