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answering two sections in online website(section 3.8 and 3.9 only)
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Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the gam ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the game to be fair? Present your computation and
explain your reasoning in addition to stating your final answer.
Note: A fair game is one in which in the long-run neither party (lottery company
and players) has an advantage.
2. There are a number of probability claims made in the Lottery tips. In this problem,
you will verify whether these claims are true. Consider the current rules (5/70 +
1/25) of the CA MEGA millions game.
(a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that
the five white numbers selected will all be even.
(b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to
approximate the probability that the sum of the five white balls will fall between
132 and 223 (both inclusive).
Discuss the appropriateness of using the Central Limit Theorem in this case. If
any of the assumptions of the theorem are violated, state what these assumtions
are and discuss how extreme (mild, moderate, severe) the violation is.
(c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether
this tip only concerns the white balls or also the gold MEGA ball.
i. Find the exact probability that in a given drawing at least one of the white
numbers is a repeat from the last drawing.
ii. Find the exact probability that in a given drawing at least one of the six
balls drawn (five white and one gold) is a repeat of the last drawing.
(d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA
million lottery numbers (five white balls and MEGA ball) will be repeated in
a drawing? Recall, that drawings take place bi-weekly and that assume that a
year has 365 days (i.e., ignore leap years).
3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the
advice of the lottery expert increase your chances of winning the lottery? (This is a
multiple choice question - Yes/No answer ONLY.)
4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the
statements made in the individual tips presented there generally truthful? Do they
hold for general (future) drawings, and not just for data collected in the past? Is
following this advice a good idea when playing the lottery? Explain why or why not.
Take a stand and defend your position with a good logical argument using the
methods of probability you have learned in this course. Provide as much numerical
evidence as necessary (you may cite your results from problem 2) to support your
3
Math 161A - Fall 2020 M. Bremer
claim(s). Make sure to provide a cohesive argument (using correct spelling and good
grammar).
5. (5 points) To study whether the drawing of lottery numbers for the MEGA million
game is truly random, we will consider some data. The data (which are available
in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls
drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions
between 5/17/2002 and 11/03/2020.
Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random
meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on.
Disclaimer: The data come from the New York State (not the California State)
MEGA millions lottery. Like California, NY has changed the rules for the MEGA
millions game several times over the last couple years. For instance, on October 19,
2013, they switched from drawing 55 white balls to drawing 75 white balls. On the
same date, the number of possible MEGA balls were reduced from 45 to 15. Another
rule change occurred in October 2017.
Note: You are welcome to look at the raw data and/or create your own additional
graphs if you wish, but that’s not required for this problem.
Grading: Your work will be graded
4 pages
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(1 pt) The histogram below gives the length of service of members of the Department of English at a particular university. ...
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(1 pt) The histogram below gives the length of service of members of the Department of English at a particular university. The classes, in years of service, are 04.9, 59.9, etc., and the vertical axis represents the number of faculty.(b) If a member of the department is chosen at random to serve on a university committee, what is the probability (in decimal form) that the chosen representitive will have between 10 and 25 years of service? Answer: ?(c) What is the probability the representative above will have less than 25 years of service given that the person has less than 35 years of service?Answer: ?
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Most Popular Content
PSYC355 Liberty University Pearson Correlation Coefficient Analysis
These homework exercises rely on the module/week's SPSS video tutorial and APA-style writing presentation, and must be sub ...
PSYC355 Liberty University Pearson Correlation Coefficient Analysis
These homework exercises rely on the module/week's SPSS video tutorial and APA-style writing presentation, and must be submitted as a Word document or Word-type document. Homework exercises will be graded based on the correctness of each answer.
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the gam ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the game to be fair? Present your computation and
explain your reasoning in addition to stating your final answer.
Note: A fair game is one in which in the long-run neither party (lottery company
and players) has an advantage.
2. There are a number of probability claims made in the Lottery tips. In this problem,
you will verify whether these claims are true. Consider the current rules (5/70 +
1/25) of the CA MEGA millions game.
(a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that
the five white numbers selected will all be even.
(b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to
approximate the probability that the sum of the five white balls will fall between
132 and 223 (both inclusive).
Discuss the appropriateness of using the Central Limit Theorem in this case. If
any of the assumptions of the theorem are violated, state what these assumtions
are and discuss how extreme (mild, moderate, severe) the violation is.
(c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether
this tip only concerns the white balls or also the gold MEGA ball.
i. Find the exact probability that in a given drawing at least one of the white
numbers is a repeat from the last drawing.
ii. Find the exact probability that in a given drawing at least one of the six
balls drawn (five white and one gold) is a repeat of the last drawing.
(d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA
million lottery numbers (five white balls and MEGA ball) will be repeated in
a drawing? Recall, that drawings take place bi-weekly and that assume that a
year has 365 days (i.e., ignore leap years).
3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the
advice of the lottery expert increase your chances of winning the lottery? (This is a
multiple choice question - Yes/No answer ONLY.)
4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the
statements made in the individual tips presented there generally truthful? Do they
hold for general (future) drawings, and not just for data collected in the past? Is
following this advice a good idea when playing the lottery? Explain why or why not.
Take a stand and defend your position with a good logical argument using the
methods of probability you have learned in this course. Provide as much numerical
evidence as necessary (you may cite your results from problem 2) to support your
3
Math 161A - Fall 2020 M. Bremer
claim(s). Make sure to provide a cohesive argument (using correct spelling and good
grammar).
5. (5 points) To study whether the drawing of lottery numbers for the MEGA million
game is truly random, we will consider some data. The data (which are available
in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls
drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions
between 5/17/2002 and 11/03/2020.
Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random
meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on.
Disclaimer: The data come from the New York State (not the California State)
MEGA millions lottery. Like California, NY has changed the rules for the MEGA
millions game several times over the last couple years. For instance, on October 19,
2013, they switched from drawing 55 white balls to drawing 75 white balls. On the
same date, the number of possible MEGA balls were reduced from 45 to 15. Another
rule change occurred in October 2017.
Note: You are welcome to look at the raw data and/or create your own additional
graphs if you wish, but that’s not required for this problem.
Grading: Your work will be graded
4 pages
Answer To Probability Project.
Below are some explanations and justifications made on some statements that stand on Statement one: I have flipped an unbi ...
Answer To Probability Project.
Below are some explanations and justifications made on some statements that stand on Statement one: I have flipped an unbiased coin three times and ...
Probability Math 114 on Webwork
(1 pt) The histogram below gives the length of service of members of the Department of English at a particular university. ...
Probability Math 114 on Webwork
(1 pt) The histogram below gives the length of service of members of the Department of English at a particular university. The classes, in years of service, are 04.9, 59.9, etc., and the vertical axis represents the number of faculty.(b) If a member of the department is chosen at random to serve on a university committee, what is the probability (in decimal form) that the chosen representitive will have between 10 and 25 years of service? Answer: ?(c) What is the probability the representative above will have less than 25 years of service given that the person has less than 35 years of service?Answer: ?
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