Suppose you are gambling on a roulette wheel.
Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 16 are red, 16 are black, and 1 is green.
On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur.
If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6.
a. Use simulation to generate 20 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these 20 outcomes, find a 95% confidence interval for the total net amount won or lost from 1000 plays of the game. Would you conclude that this strategy is a winning one for you?
b. Repeat part a, but with slightly changed rules. Now your betting strategy is the same, but if red occurs, your net gain is $5 (you win $11 from red, nothing from green). Comment on whether this slight change makes much of a difference in the mean total from 1000 bets.