Question

In: Statistics and Probability

If you bet $1 in Kentucky’s Pick 4 lottery, you either lose $1 or gain $4999. (The winning prize is $5000, but your $1 bet is not r

If you bet $1 in Kentucky’s Pick 4 lottery, you either lose $1 or gain $4999. (The winning prize is $5000, but your $1 bet is not returned, so the net gain is $4999.) The game is played by selecting a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $1 on 1234, what is the expected value of your gain or loss?

 

 

Solutions

Expert Solution

Here if, The game is played by selecting a four-digit number between 0000 and 9999.

Then,

For this bet, there are two outcomes: You either lose $1 or you gain $4999.

Probability of losing = 9,999 /10,000

Probability of winning = 1 /10,000

 

For lose : x = -$1 , p(x) = 0.9999 ,x*p(x) = -$0.9999

For gain: x = $4999 , p(x) = 0.0001 ,x*p(x) = $0.4999

 

Then total = lose - gain = -$ 0.5

 

The Probability of the winning is 1/10,000 and the value of gain or loss is -$ 0.5.

The Probability of the winning is 1/10,000 and the value of gain or loss is -$ 0.5.

Junaid answered 1 year ago
Next > < Previous

Related Solutions

Assume that you just won the state lottery. Your prize can be taken either in the...
Assume that you just won the state lottery. Your prize can be taken either in the form of $40,000 at the end of each of the next 25 years or as a single payment of $500,000 paid immediately. If you expect to be able to earn 5% annually on your investments over the next 25 years, which alternative should you take?
1. In an instant lottery, your chances of winning are 0.1. If you play the lottery...
1. In an instant lottery, your chances of winning are 0.1. If you play the lottery six times and outcomes are independent, determine the probability that (i) you win at most once. (ii) you lose all six times. (iii) you win exactly two times. Please show work will rate!!!
1.As an employee in the Lottery Commission, your job is to design a new prize. Your...
1.As an employee in the Lottery Commission, your job is to design a new prize. Your idea is to create two grand prize choices: (1) receiving $50,000 at the end of each year beginning in one year for 20 consecutive years, or (2) receiving $500,000 today followed by a one-time payment at the end of 20 years. Using an interest rate of 3%, which of the following comes closest to the amount prize (2) needs to pay at the end...
1.As an employee in the Lottery Commission, your job is to design a new prize. Your...
1.As an employee in the Lottery Commission, your job is to design a new prize. Your idea is to create two grand prize choices: (1) receiving $50,000 at the end of each year beginning in one year for 20 consecutive years, or (2) receiving $500,000 today followed by a one-time payment at the end of 20 years. Using an interest rate of 3%, which of the following comes closest to the amount prize (2) needs to pay at the end...
In a​ lottery, you bet on a six-digit number between 000000 and 111111. For a​ $1...
In a​ lottery, you bet on a six-digit number between 000000 and 111111. For a​ $1 bet, you win ​$700,000 if you are correct. The mean and standard deviation of the probability distribution for the lottery winnings are μ=0.70 (that is, 70 cents) and σ=700.00. Joan figures that if she plays enough times every​ day, eventually she will strike it​ rich, by the law of large numbers. Over the course of several​ years, she plays 1 million times. Let x...
INVESTING YOUR OWN PORTFOLIO You have won the jackpot of a European Lottery with a prize...
INVESTING YOUR OWN PORTFOLIO You have won the jackpot of a European Lottery with a prize of €30 000. After distributing a portion of the prize to a local charity, you decide that it is a good idea to invest the rest of the prize. However, you are doubtful about which asset class or financial vehicle is more suitable given the current international context. Bear in mind that you are in your early twenties and that your financial restrictions are...
INVESTING YOUR OWN PORTFOLIO You have won the jackpot of a European Lottery with a prize...
INVESTING YOUR OWN PORTFOLIO You have won the jackpot of a European Lottery with a prize of €30 000. After distributing a portion of the prize to a local charity, you decide that it is a good idea to invest the rest of the prize. However, you are doubtful about which asset class or financial vehicle is more suitable given the current international context. Bear in mind that you are in your early twenties and that your financial restrictions are...
1. You have just won the prize in the State lottery. A recent innovation is to...
1. You have just won the prize in the State lottery. A recent innovation is to offer prize winners a choice of payoffs. You must choose one of the following prizes: a. $1,000,000 paid immediately b. $600,000 paid exactly one year from today, and another $600,000 paid exactly 3 years from today c. $70,000 payment at the end of each year forever (first payment occurs exactly 1 year from today) d. An immediate payment of $600,000, then beginning exactly 5...
Manuel just won the lottery and the prize was $ 1 million. You have the option...
Manuel just won the lottery and the prize was $ 1 million. You have the option of receiving a lump sum of $ 312,950 or $ 50,000 per year for the next 20 years. If Miguel can invest the single amount at 9% or invest the annual payments at 7%; Which one should I choose? a. one-time amount of 312,950 b. b. annual payments of 50,000
The odds on​ (against) your bet are 1 to 6. If you bet ​$18 and​ win,...
The odds on​ (against) your bet are 1 to 6. If you bet ​$18 and​ win, how much will you​ gain?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT