Expected Value Probability

Task 2.1: In a bag, there are 20 balls, 12 green balls, and 8 white balls.

You draw three balls at random.

If you get 3 white balls, you win $5, if you draw 3 green balls you lose $1, otherwise, you neither win nor lose.

You can draw the balls in two ways:

1)draw a table with a replacement,

2.draw a table without replacement

Which way you should choose to draw so as to maximize winning? Explain why. Draw the tree diagram by hand and find All possible outcomes.

I know that the first, second, and third draw is independent. what is the relationship between the first draw, second draw, and third draw? I also know this a conditional probability. what is the independent events and which is not. what is the characteristic between the independent event and why can we multiply it together. What is the multiplication rule?