A contestant on a quiz show is presented with two questions, questions 1 and 2, which he is to attempt to answer in some order he chooses. If he decides to try question i first, then he will be allowed to go on to question j, j not = to i, only if his answer to question i is correct. If his initial answer is incorrect, he is not allowed to answer the other question. if he is 60% certain of answering question 1, worth$200, correctly and he is 80% certain of answering question 2, worth $100, correctly. Which question he should try first as to maximize his expected winnings?

You are using cash to pay a $20 parking ticket. In your wallet you have one  $5-dollar bill, two $10-dollar bills, and three $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?

In a certain class of 25 students, 12% received A’s, 30% received B’s, 42% received C’s, and 12% received D’s.  How many students failed the class?

A particular gambling game pays 4 to 1 and has a 20% chance to win. Someone will bet $10, 125 times, and keep track of the total amount won or lost. Which of the following boxes will produce the right answers? Check ALL answers that apply. a. 1 ticket labeled $10 and 4 tickets labeled -$10 b. 20 tickets labeled $10 and 80 tickets labeled -$10 c. 20 tickets labeled 1 and 80 tickets labeled 0 d. 1 ticket labeled $40 and 4 tickets labeled -$10 e. 20 tickets labeled $40 and 80 tickets labeled -$10 f. 1 ticket labeled 1 and 4 tickets labeled 0

A new game is being introduced at the Hard Rock Cafe.  A ball is spun around a wheel until it comes to rest in one of many spots.  Whatever is listed in that spot will be the player's winnings.  If the wheel has 15 spots labeled $1, 9 spots labeled $2, and 9 spots labeled $10, how much should a player expect to win on average?

A new game is being introduced at the Hard Rock Cafe.  A ball is spun around a wheel until it comes to rest in one of many spots.  Whatever is listed in that spot will be the player's winnings.  If the wheel has 8 spots labeled $1, 16 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average?

Martha has $20. She is deciding whether to take the following bet: A coin will be flipped, and if the result is heads she has to pay $20, but if it is tails she receives $70. Martha has the following utility over wealth: u = W", where a is some positive number. For which values of a will she take the bet?

A new game is being introduced at the Hard Rock Cafe.  A ball is spun around a wheel until it comes to rest in one of many spots.  Whatever is listed in that spot will be the player's winnings.  If the wheel has 11 spots labeled $1, 10 spots labeled $2, and 5 spots labeled $10, how much should a player expect to win on average?

A chef is trying out a new recipe he has been working on and wants to see if it will sell better than his old one. To find out, he performs an experiment where he randomly assigns 20 people to try his new recipe and 20 people to try his old one. He asks each group how much they would be willing to pay for their food, and he finds that the group with the old recipe would pay an average of $20.00 and the second would pay an average of $26.00. He then performs an independent samples t-test between these groups. a. Suppose the sample variance for the price of the chef’s old recipe is $2.00, and the sample variance for the new recipe is $3.00. Perform a one-tailed t-test at a significance level of α = 0.01 and explain what the result means (how does the new recipe compare to the old one?). b. To evaluate the magnitude of effect size, compute the estimated Cohen’s d. Briefly describe what it means, and comment on the strength of the effect: is it weak, moderate or strong?

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 flip a fair coin. She will give you $8$ for heads and $⁢22 for tails. Your mother says she wants you to roll a six-sided die. She will give you $4$ times the number that appears on the die. Determine the expected value of each game and decide which offer you should take.