Investigate the winning chances of some games. An amusement park offers the following game. A hat contains 20 balls: 5 red, 5 yellow, 3 green, and 7 brown. At a cost of 2n units of money you can draw...

Investigate the winning chances of some games.

An amusement park offers the following game. A hat contains 20 balls: 5 red, 5 yellow, 3 green, and 7 brown. At a cost of 2n units of money you can draw 4 ≤ n ≤ 10 balls at random from the hat (without putting them back). Before you are allowed to look at the drawn balls, you must choose one of the following options:

1. win 60 units of money if you have drawn exactly three red balls

2. win 7 + 5√ n units of money if you have drawn at least three brown balls

3. win n

3 − 26 units of money if you have drawn exactly one yellow ball and one brown ball

4. win 23 units of money if you have drawn at least one ball of each color

For each of the 4n different types of games you can play, compute the net income (per play) and the probability of winning. Is there any of the games (i.e., any combinations of n and the options 1-4) where you will win money in the long run? Name of program file: draw_balls.py.