Statistics

Having trouble with these four questions:

1. Given the rules of the different games of chance described in the sheet you downloaded, think about your odds of winning in each of these three scenarios:
A. : Either roll or a 7 or 11 on the first roll, OR match the point value on a subsequent roll. What's the likelihood of winning after one roll? Explain your answer.B. Roulette: You bet on numbers 1-18. What's the likelihood of winning after one trial? Explain your answer.
C. Chuck-A-Luck: To win any money, at least two of your dice must show the same number. What's the likelihood of winning anything after one roll? Explain your answer.
D. To win at these games seems quite easy! Use you knowledge of probability to compute the likelihood of winning each of these games and rank them from best to worst odds. Explain your answer.
2. How would a probability to win of .42 translate into an expected amount won if you had $5.00? Assume that each time you win, you double your money, and each time you lose, you lose what you bet.
A. Imagine a scenario where you'd put one dollar on each of five games, each with a probability of winning of .42, and you do NOT roll your winnings into another game. (Hint: Your expected "winnings" would always be negative, but how much would you expect to lose?)
3. If people win every day in Las Vegas gambling casinos, why do the casinos always take in more money than they pay out? Use a specific probability example to explain your answer.
4. There are many ways to win each of these games. Some of these "wins" are harder and thus provide better payoffs (for example, spinning a number between 1-4 in Roulette is harder, and thus pays better odds, than simply spinning a number between 1-18). Here are two modified game scenarios:
A. You win if you spin a 3, 13, 23, or 33 in Double Roulette. You lose on any other roll.
B. You win if you roll two or more of your chosen value (you choose 3 and roll 2+ 3's) in a roll of Chuck-A-Luck. You lose with any other combination of the dice.

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