Gambling is generally a losing proposition

Assignment Help Mathematics

Reference no: EM13118261

Use excel solver to find solution for LP problem
A couple has agreed to attend a "Casino Night" as part of a fundraiser for the local hospital. They do not like to gamble because they believe that gambling is generally a losing proposition. However, for the sake of the charity, they have decided to attend and spend $300 on the games. There will be four games, each involving standard decks of cards.

The first game, Jack in 52, is won if you select the Jack of a particular suit from the deck. The probability of actually doing this is 4 in 52 (4/52 or .0769). Gamblers may place bets of $1, $2, or $4 on this game. If they win, the payouts are $12.00 for a $1 bet, $24.55 for a $2 bet, and $49 for a $4 bet.
The second game, Red Face in 52, is won if you select a red face card (including the Jack, Queen, or King) from the deck. The probability of winning is 6 in 52 (.1154). Again, bets may be placed in denominations of $1, $2, and $4. Payouts are $8.10, $16.35, and $32.50, respectively.

The third game, Face in 52, is won if you select 1 of the 12 face cards from the deck. The probability of winning is 12 in 52 (.2308). Payouts are $4, $8.15, and $16 for $1, $2, and $4 bets.

The last game, Red in 52, is won if you select a red card from the deck. The probability of winning is 26 in 52 (.5). Payouts are $1.80, $3.80, and $7.50 for $1, $2, and $4 bets.

Given that they can calculate the expected return or loss for each type of game and level of wager, they have decided to see if they can minimize their expected loss by planning their evening using LP. For example, a $1 bet in Jack in 52 has a return of $12.00, but there is only a 1 in 13 chance of winning. Therefore, the expected value of the dollar bet is ($12.00*(1/13)) or $.9231. This computes to an expected loss of $1-.9231, or $.0769.
The couple wants to appear generous. Therefore, they will place at least 20 bets (of any value) on each of the four games. Further, they will spend at least $26 on 1-dollar bets, at least $50 on 2-dollar bets, and at least $72 on 4-dollar bets. They will bet exactly the agreed-upon $300. What should be their gambling plan, and what is their expected loss for the evening?

Reference no: EM13118261

Questions Cloud

Find variance-standard deviation for producing weather tire : What is the variance and standard deviation (of profit, NOT of tire life) for producing an all weather tire? Of producing a high performance tire?

Rules for radical expressions : Five outside of the square root symbol then 3 under the square root symbol plus 15 outside of the square root symbol then 3 under the square root symbol plus 12 outside the square root symbol then 3 under the square root symbol plus 32.

What minimum mass of succimer in miligrams is needed : A modern chealting agent used for this purpose is succimer (C4H6O4S2). Suppose you are trying to determine the appropriate dose for succimer treatment of lead poisoning.

Expalin how far above the floor should the bottom edge : The top of her head is 0.12m above her eyes. What is the height of the shortest mirror in which she can see her entire image? Expalin how far above the floor should the bottom edge of the mirror be placed?

Gambling is generally a losing proposition : Use excel solver to find solution for LP problem A couple has agreed to attend a "Casino Night" as part of a fundraiser for the local hospital. They do not like to gamble because they believe that gambling is generally a losing proposition.

Illustrate what is the tension t in each of the cables : Each cable has a length of l = 2.90 m. Illustrate what is the tension T in each of the cables? Use 9.80 m/s2 for the magnitude of theacceleration due to gravity.

What is the specific heat capacity of the metal : A piece of metal of mass 20 g at 99?C is placed in a calorimeter containing 55.8 g of water at 23?C. The final temperature of the mixture is 30.4?C.

Find normal probability distributions : Find Normal Probability Distributions, How many ways can 15 girls be chosen to form a baseball team of 9 players?

Illustrate what is the angle among the velocity of particle : A charged particle m=6g q=-80 c moves in a region of uniform field along a helical path (radius = 3.0 cm, pitch = 9.0 cm) as shown. Illustrate what is the angle among the velocity of the particle and the magnetic field?

User Account

All Pages