what should we pay in return each time the sum does not exceed four to make the game fair?
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- A magazine distributor offers a first prize of$100,000, two second prizes of $40,000 each, and two third prizes of $10,000 each. A total of 2,000,000 entries are re-ceived in the contest. Find the expected payback if you submit one entry to the contest. If it would cost you $1 in time, paper,and stamps to enter, would it be worth it?A and B play for a prize of $. 1,000. A is to throw a dice first and is to win if he throws 6. If he fails B is to throw and is to win if he throws 6 or 5. If he fails, A is to throw again and to win if he throws 6, 5 or 4, and so on. Find their respective expectations.An option to buy a stock is priced at $210. If the stock closes above 30 on May 15, the option will be worth $900. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $180. A trader thinks there is a 45% chance that the stock will close in the 20–30 range, a 25% chance that it will close above 30, and a 30% chance that it will fall below 20 on May 15. How much do they expect to gain? Should they buy the stock option? Explain.
- Would you pay $10 per throw of two dice if you were to receive a number of dollars equal to the product of the numbers on the dice? Hint: What is your expectation? If it is more than $10, then the game would be favorable for you.A City of Quincy raffle offers one $800 prize, two$400 prizes and seven $100 prizes. Two thousand tickets are sold at $50each. Find the expectation (from the perspective of the player) if a personbuys one ticket.A game costs $1 to play where you win $5 when a coin lands on heads but lose $6 when a coin lands on tails. Calculate the expected payoff to the nearest cent, being sure to show all work.
- One option in a roulette game is to bet $28 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 $28 you paid to play the game and you are awarded $28. If the ball lands elsewhere, you are awarded nothing and the $28 that you bet is collected. Find the expected payback for this roulette game if you bet $28 on red.You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest centA lottery offers one $2000 prize, one $900 prize and five $200 prizes.One thousand tickets are sold at $5 each. Find the expectation if a person buys oneticket.
- You flip two fair coins. If both coins land heads you win $2. Otherwise you lose $1. What is the expectation of this game? Round your answer to the nearest cent.Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10For the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. If it costs $3 to play the game, determine (a) the expectation of a person who plays the game and (b) the fair price to play the game. $4 S7
