Suppose a gambler plays roulette 400 times, betting $1 on each play on red. Recall from the previous week's that the gambler has a 18 chances in 38 to win. Thus the box model contains 18 +$1 tickets and 20 -$1 tickets.  The gambler can expect to lose $, give or take $ or so. Hint: This problem is exactly the same as the previous problem, you can reuse some of your previous calculations instead of starting over from scratch.

You are a contestant on a game show. There are three closed doors in front of you. The game show host tells you that behind one of these doors is a million dollars in cash, and that behind the other two doors there are trashes. You do not know which doors contain which prizes, but the game show host does. The game you are going to play is very simple: you pick one of the three doors and win the prize behind it. After you have made your selection, the game show host opens one of the two doors that you did not choose and reveals trash. At this point, you are given the option to either stick with your original door or switch your choice to the only remaining closed door. To maximize your chance to win a million dollars in cash, should you switch? Choices: A) Yes B) No C) It doesn't matter because the probability for you to win a million dollars in cash stays the same no matter if you switch or not.

A game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take.   The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?

At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1–4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X       P(X)       (b) Compute your expected net winnings for the game. Round your answer to the nearest cent.

You are using cash to pay a $20 parking ticket. In your wallet you have one $5-dollar bill, three $10-dollar bills, and two $20 dollar bills, and you draw out one bill at a time at random until you have at least $20. If you keep track of each bill as you draw it out of the wallet, how many different ways are there for you to get at least $20?

One option in a roulette game is to bet $7 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $7 you paid to play the game and you are awarded $7. If the ball lands elsewhere, you are awarded nothing and the $7 that you bet is collected. Complete parts (a) through (b) below. III a. What is the expected value for playing roulette if you bet $7 on red? $ (Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. O A. This value represents the expected loss over the long run for each game played. OB. Over the long run, the player can exper to break even. OC. This value represents the expected win over the long run for each game played.

Mickey and Minnie are playing a game. They spin a spinner that has 11 equally sized pieces, 3 red, 2 blue, 1 green and 5 yellow. If the spinner lands on yellow, Minnie wins $7. If it lands on blue, Minnie wins $ 4. If it lands on any other section, Minnie loses money. In order for the game to be fair, Minnie must lose $ Blank 1. Calculate the answer by read surrounding text. if