One option in a roulette game is to bet $24on 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 $24 you paid to play the game and you are awarded $24. If the ball lands elsewhere, you are awarded nothing and the $24 that you bet is collected. Find the expected payback for this roulette game if you bet $24 on red.
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- In a certain game, suppose there is no cost to playing the game, and a player has a probability 0.07 of winning a prize worth $1,787 ,and a probability of 0.33 of winning another prize What is the expected payment of playing the game? (please do not round your worth $70 final answer, and enter it in the box provided below as is).Find the expected payback for a game in which you bet $88 on any number from 0 to 499. If your number comes up, you get $1000.Suppose you play a game of chance in which five numbers are chosen from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A computer randomly selects five numbers from zero to nine with replacement. You pay $2 to play and could profit $100,000 if you match all five numbers in order (you get your $2 back plus $100,000). Over the long term, what is your expected profit of playing the game? Can give at least an explanation? I don't really get this one.
- You draw and keep a single bill from a hat that contains a $1.$10, S20 and $100 bill. What is the expected value of the game to you? The expected value of the game to you is dollars. (Type an integer or a decimal.)Suppose you won the lottery and had two options: (1) receiving $0.8 million or (2) taking a gamble in which, at the flip of a coin, you receive $1.6 million if a head comes up but receive zero if a tail comes up. What is the expected value of the gamble? Enter your answer in millions. For example, an answer of $500,000 should be entered as 0.5. Round your answer to one decimal place. $ million Would you take the sure $0.8 million or the gamble? If you chose the sure $0.8 million, would that indicate that you are a risk averter or a risk seeker? Suppose the payoff was actually $0.8 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $856,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $1,920,000 at the end of the year. The expected profit on the T-bond investment is $56,000. What is the expected dollar profit on the stock investment? Round your answer to the nearest…So, what could be better than winning a SuperLotto Plus jackpot? Choosing how to receive your winnings! Before playing a SuperLotto Plus jackpot, you have a choice between getting the entire jackpot in 26 annual graduated payments or receiving one lump sum that will be less than the announced jackpot. (See Figure 2.29.) What would these choices come out to for an announced jackpot of $7 million?• Lump-sum cash-value option: The winner would receive the present cash value of the announced jackpot in one lump sum. In this case, the winner would receive about 49.43%, or $3.46 million, in one lump sum (less tax withholdings).This cash value is based on average market costs determined by U.S. Treasury zero-coupon bonds with 5.3383% annual yield.• Annual-payments option: The winner would receive the jackpot in 26 graduated annual payments. In this case, the winner would receive $175,000 as the first payment (2.5% of the total jackpot amount) immediately. The second payment would be $189,000.…
- 3. Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,950 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 8% per year, the winner would be better off accepting the , since that choice has the greater present value. At an interest rate of 10% per year, the winner would be better off accepting , since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend? The lump sum is…Mr. John is watching an old game show rerun on television called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. One of the curtains will yield a gag prize worth Rs.14,700/-, and the other will give a car worth Rs. 63,600. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 60 percent. What is the expected value of the selection? (a) Rs. 24,260; (b) Rs. 34,260; (c) Rs. 43,620; (d) Rs. 32,620; (e) Rs. 26,420Suppose you have won $1,122,000 in the lottery. You have two options. Option 1: Take a lump sum of $953,700. Option 2: Receive the entire amount of your winnings in 240 monthly installments of $4,675.00. Either way, you have decided to be very disciplined about this money and invest all you receive. a. Suppose you take Option 1 and deposit the lump sum of $953,700 into an account that pays an APR of 4% compounded monthly. Find the account balance after 20 years. Option 1: $ _____________ b. Suppose you take Option 2 and deposit your monthly installments of $4,675 into an account with the same terms: APR of 4% compounded monthly. Find the account balance after 240 monthly deposits. Option 2: $ _____________ c. How much do you gain by taking the money in a lump sum (Option 1)? Gain by Choosing Option 1: $ _____________
- The questions in this section contribute to your assignment grade. Stars indicate the difficulty of the questions, as described on Canvas. 2. Mark and Elyse buy a lottery ticket together. They win a promotion that guarantees them free apples for life. The apples can only be delivered to one recipient. Mark decides to buy Elyse out of her share of the win. That is: Mark will receive all the apples (for life) and Elyse will receive cash (once). The deliveries of apples are valued at $1000 per year. The friends consult an actuarial table, and decide that they both can reasonably be expected to live another 50 years. So, Elyse proposes that Mark pays her $25,000 for her half of the windfall. Mark, sensing an opportunity for calculus and for profit, declines her offer. He explains his objection: "If I pay you a dollar now, and get a dollar back 50 years later, that's not a good deal for me." Mark and Elyse agree on a future discounting rate of 10% per year. They calculate it as follows:¹ D…You see on TV that the Mega Millions is up to $2 million! You decide to buy a ticket ......... and you WIN!!! Unfortunately, you do not get that amount right away. Instead, this is the future value of an annuity. Let us examine some choices you have regarding your big win. a) You could choose to collect your winnings today, in the present day. The lottery people could invest this present value and earn 2.7% interest, compounded annually, and have the $2 million in 25 years. How much would they give you today? b) The interest rate in part (a) is very conservative. You have a “friend” who advises you to take the money today and invest it with him, at 6.6% compounded quarterly, for those 25 years. How much would you have in 25 years if you did this? (What is the future value of the amount you computed in part (a)?) c) Otherwise, you could choose to take the annuity. They will pay you nothing in the present day but will pay you A dollars each month for 25 years. Assume 2.7% interest…In a certain state lottery, a lottery ticket costs 2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies: a. A realistic estimate of the chances of winning is 1 in 250,000. Use the expected value approach to recommend a decision. b. If a particular decision maker assigns an indifference probability of 0.000001 to the 0 payoff, would this individual purchase a lottery ticket? Use expected utility to justify your answer.