You have 80 dollars and play the following game. An urn contains two white balls and two black balls. You draw the balls out one at a time without replacement until all the balls are gone. On each draw, you bet half of your present fortune that you will draw a white ball. If you do, you win an amount equal to your bet. If you do not, you lose your bet. What is your expected final fortune? Gerolamo Cardano in his book, The Gambling Scholar, written in the early 1500s, considers the following carnival game. There are six dice. Each of the dice has five blank sides. The sixth side has a number between 1 and 6--a different number on each die. The six dice are rolled and the player wins a prize depending on the total of the numbers which turn up. Find, as Cardano did, the expected total without finding its distribution.

A jar on your desk contains ten black, eight red, seven yellow, and five green jellybeans. You pick a jellybean without looking. Find the odds of picking a green jellybean.

A modified roulette wheel has 40 slots. One slot is​ 0, another is​ 00, and the others are numbered 1 through 38​, respectively. You are placing a bet that the outcome is an even number.​ (In roulette, 0 and 00 are neither odd nor​ even.)Question content area bottomPart 1a. What is your probability of​ winning?The probability of winning is enter your response here.​(Type an integer or a simplified​ fraction.)Part 2b. What are the actual odds against​ winning?The actual odds against winning are enter your response here​:enter your response here.Part 3c. When you bet that the outcome is an even ​number, the payoff odds are​ 1:1. How much profit do you make if you bet ​$16 and​ win?If you​ win, the payoff is ​$enter your response here.Part 4d. How much profit should you make on the ​$16 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against​ winning?​$enter your response here ​(Round to the nearest cent as​ needed.)

There are 50 tickets sold for a raffle for a Student ArtAuction, and there is one prize to be awarded. If Diontebuys a ticket, find the odds that he’ll win.

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws two red cards in succession from a standard deck of 52 cards without replacing the first card, you give him $50. Otherwise, he pays you $20. If the same bet was made 15 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary. Answer O Win ⒸLose Keypad Keyboard Shortcuts

Suppose you play a game where you roll 2 six-sided dice. If you roll a 7, you will lose some money, but if you roll anything else you will win 100. How much money would you have to lose in order for you average 0 per roll?

Please help. Thanks!

A restaurant will select 1 card from a bowl to win a free lunch. Jo puts 5 cards in the bowl. The bowl has 100 cards. What are the odds of Jo winning a free lunch?    1/5   1/10   1/20    1/500

How many outcomes are possible if you toss a coin six times?

Casino Games Many casinos have a game called the Big Six Money Wheel. which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts. as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player’s bet, the player wins that amount for each dollar bet. If a player bets $1 on the $20 denomination, find the player’s expectation.If a player bets $1 on the $5 denomination, find the player’s expectation.