Question

In: Statistics and Probability

For a multistate​ lottery, the following probability distribution represents the cash prizes of the lottery with...

For a multistate​ lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts​ (a) through​ (c) below. x (cash prize, $) P(x) 14,000,000 0.00000000547 200,000 0.00000032 10,000 0.000001604 100 0.000165836 7 0.004321645 4 0.008019353 3 0.01545068 0 0.97204055653 If the grand prize is ​$14,000,000​, find and interpret the expected cash prize. If a ticket costs​ $1, what is your expected profit from one​ ticket?

x (cash prize, $)   P(x)
14,000,000   0.00000000547
200,000   0.00000032
10,000   0.000001604
100   0.000165836
7   0.004321645
4   0.008019353
3   0.01545068
0   0.97204055653

If the grand prize is

$14,000,000​,

find and interpret the expected cash prize. If a ticket costs​ $1, what is your expected profit from one​ ticket?

Solutions

Expert Solution

Let X denotes the cash prize of the lottery. The expected cash prize is E[X] and expected profit from one ticket of $1 is E[X]-1.The detail solution is given in the images...


Related Solutions

For a multistate? lottery, the following probability distribution represents the cash prizes of the lottery with...
For a multistate? lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts? (a) through? (c) below. x? (cash prize,? $) ?P(x) Copy to Clipboard + Open in Excel + Grand prizeGrand prize 0.000000008390.00000000839 ?200,000 0.000000360.00000036 ?10,000 0.0000018710.000001871 100 0.0001479450.000147945 7 0.0054037740.005403774 4 0.0064119730.006411973 3 0.011546880.01154688 0 0.976487188610.97648718861 ?(a) If the grand prize is ?$12 comma 000 comma 00012,000,000?, find and interpret the expected cash prize. If a ticket costs? $1, what...
One state lottery has 1,100 prizes of $1; 135 prizes of $10; 15 prizes of $50;...
One state lottery has 1,100 prizes of $1; 135 prizes of $10; 15 prizes of $50; 5 prizes of $310; 2 prizes of $1,150; and 1 prize of $2,500. Assume that 22,0000 lottery tickets are issued and sold for $1. Round final answer to four decimals. 1. What is the lottery's expected profit per ticket? 2. What is the lottery's standard deviation of profit per ticket?
One state lottery has 1,100 prizes of $1; 120 prizes of $10; 30 prizes of $50;...
One state lottery has 1,100 prizes of $1; 120 prizes of $10; 30 prizes of $50; 5 prizes of $285; 2 prizes of $1,180; and 1 prize of $2,400. Assume that 34,000 lottery tickets are issued and sold for $1. Round to 4 decimal places for the answers What is the lottery's expected profit per ticket? What is the lottery's standard deviation of profit per ticket?
One state lottery has 1,000 prizes of $1; 130 prizes of $10; 20 prizes of $55;...
One state lottery has 1,000 prizes of $1; 130 prizes of $10; 20 prizes of $55; 5 prizes of $300; 2 prizes of $1,010; and 1 prize of $2,500. Assume that 31,000 lottery tickets are issued and sold $1 What is the lottery's expected profit per ticket? What is the lottery's standard deviation of profit per ticket?
The following data set provides information on the lottery sales, proceeds, and prizes by year in...
The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa. FYI Sales Proceeds Prizes 1986 $85,031,584 $27,631,613 $39,269,612 1987 $98,292,366 $31,157,797 $47,255,945 1988 $128,948,560 $40,090,157 $65,820,798 1989 $172,488,594 $49,183,227 $92,563,898 1990 $168,346,888 $50,535,644 $90,818,207 1991 $158,081,953 $44,053,446 $86,382,329 1992 $166,311,122 $45,678,558 $92,939,035 1993 $207,192,724 $56,092,638 $116,820,274 1994 $206,941,796 $56,654,308 $116,502,450 1995 $207,648,303 $58,159,175 $112,563,375 1996 $190,004,182 $51,337,907 $102,820,278 1997 $173,655,030 $43,282,909 $96,897,120 1998 $173,876,206 $42,947,928 $96,374,445 1999 $184,065,581 $45,782,809 $101,981,094 2000 $178,205,366 $44,769,519...
As a winner of a lottery you can choose one of the following prizes: 1) £1...
As a winner of a lottery you can choose one of the following prizes: 1) £1 million now. 2) £1.5 million at the end of six years. 3) £80,000 a year forever, starting in one year. 4) £150,000 for each of the next ten years, starting in one year. If the discount rate is 8 per cent, which is the most valuable prize?
The following data set provides information on the lottery sales, proceeds, and prizes by year in...
The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa. FY Sales Proceeds Prizes 1992 $166,311,122 $45,678,558 $92,939,035 1993 $207,192,724 $56,092,638 $116,820,274 1994 $206,941,796 $56,654,308 $116,502,450 1995 $207,648,303 $58,159,175 $112,563,375 1996 $190,004,182 $51,337,907 $102,820,278 1997 $173,655,030 $43,282,909 $96,897,120 1998 $173,876,206 $42,947,928 $96,374,445 1999 $184,065,581 $45,782,809 $101,981,094 2000 $178,205,366 $44,769,519 $98,392,253 2001 $174,943,317 $44,250,798 $96,712,105 2002 $181,305,805 $48,165,186 $99,996,233 HelpCopy to ClipboardDownload CSV Create a graph using the sales and year. What approximate range...
The following data set provides information on the lottery sales, proceeds, and prizes by year in...
The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa. FY Sales Proceeds Prizes 1992 $166,311,122 $45,678,558 $92,939,035 1993 $207,192,724 $56,092,638 $116,820,274 1994 $206,941,796 $56,654,308 $116,502,450 1995 $207,648,303 $58,159,175 $112,563,375 1996 $190,004,182 $51,337,907 $102,820,278 1997 $173,655,030 $43,282,909 $96,897,120 1998 $173,876,206 $42,947,928 $96,374,445 1999 $184,065,581 $45,782,809 $101,981,094 2000 $178,205,366 $44,769,519 $98,392,253 2001 $174,943,317 $44,250,798 $96,712,105 2002 $181,305,805 $48,165,186 $99,996,233 HelpCopy to ClipboardDownload CSV Create a graph using the sales and year. What approximate range...
1. The following probability distribution represents the number of people living in a Household (X), and...
1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable. Show Your Calculations for the Mean.     X      1         2        3          4        5                P(X)    .33      .29      .27        .07       .04      2. Use the binomial formula to compute the probability of a student getting 8 correct answers on a 10...
The following represents the probability distribution of future returns for stock A and stock B. State...
The following represents the probability distribution of future returns for stock A and stock B. State of Economy Probability Return on Security A Return on Security B Boom 0.20 18% 4% Normal 0.60 8% 8% Recession 0.20 −4% 12% a. What is the expected return for Security A and Security B? b. What is the expected return on a portfolio consisting of 50% investment in Security A and 50% in security B? c. What is the standard deviation of a...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT