Question

In: Math

A group of 20 people have a Russian roulette party. Each person at the party plays...

A group of 20 people have a Russian roulette party. Each person at the party plays (pulls the trigger) three times.

In between the times they re-spin the barrel. What is a box model for the fraction of people who survive the party? What is the expected value and standard error?

If they do not re-spin the barrel, what is a box model for the fraction of survivors? What is the expected value and standard error?

Expert Solution

The odds of dying in one trigger is: a one in six chance.

Probability of surviving 3 triggers = (5/6)^3 = 0.5787

Probability of dying = 0.4213

Now, making a probability distribution for number of people surviving with re-spin of barrel:

People suviving	Probability
1	8.5242E-07
2	1.1124E-05
3	9.1678E-05
4	0.00053521
5	0.00235255
6	0.00807883
7	0.02219458
8	0.04954147
9	0.0907353
10	0.13710004
11	0.17120385
12	0.17637759
13	0.14909348
14	0.10239937
15	0.05626339
16	0.02415152
17	0.00780592
18	0.00178707
19	0.0002584
20	1.7747E-05

formula used in excel:

Expected value is sumproduct of above two columns = 11.57

A	B
People suviving	Probability	A*B	A^2*B
1	8.5242E-07	8.52416E-07	8.52416E-07
2	1.1124E-05	2.22471E-05	4.44942E-05
3	9.1678E-05	0.000275033	0.000825099
4	0.00053521	0.002140825	0.008563298
5	0.00235255	0.011762772	0.058813862
6	0.00807883	0.048472963	0.290837777
7	0.02219458	0.15536206	1.087534423
8	0.04954147	0.396331787	3.170654295
9	0.0907353	0.816617693	7.349559233
10	0.13710004	1.3710004	13.710004
11	0.17120385	1.883242307	20.71566538
12	0.17637759	2.116531065	25.39837278
13	0.14909348	1.938215261	25.19679839
14	0.10239937	1.433591169	20.07027637
15	0.05626339	0.843950845	12.65926268
16	0.02415152	0.38642438	6.182790075
17	0.00780592	0.13270068	2.255911557
18	0.00178707	0.032167262	0.579010723
19	0.0002584	0.004909533	0.093281133
20	1.7747E-05	0.00035494	0.007098805
		11.57407407	138.8353052
		Var	4.87611454
		SD	2.208192596

Standard error = 2.21

Now, if we don't respin the barrel

Probability of surviving 3 triggers = 5/6*4/5*3/4 = 0.5

Now, updated excel calculations:

A	B
People suviving	Probability	A*B	A^2*B
1	1.9073E-05	1.90735E-05	1.90735E-05	Survive	0.5
2	0.0001812	0.000362396	0.000724792	Die	0.5
3	0.00108719	0.003261566	0.009784698
4	0.00462055	0.018482208	0.073928833
5	0.01478577	0.073928833	0.369644165
6	0.03696442	0.221786499	1.330718994
7	0.07392883	0.517501831	3.622512817
8	0.12013435	0.961074829	7.688598633
9	0.16017914	1.441612244	12.97451019
10	0.17619705	1.76197052	17.6197052
11	0.16017914	1.76197052	19.38167572
12	0.12013435	1.441612244	17.29934692
13	0.07392883	0.961074829	12.49397278
14	0.03696442	0.517501831	7.245025635
15	0.01478577	0.221786499	3.326797485
16	0.00462055	0.073928833	1.182861328
17	0.00108719	0.018482208	0.31419754
18	0.0001812	0.003261566	0.058708191
19	1.9073E-05	0.000362396	0.006885529
20	9.5367E-07	1.90735E-05	0.00038147
		10	105
		Var	5
		SD	2.236067977

Expected value is sumproduct of above two columns = 10

Standard error = 2.236

milcah answered 5 months ago

10 couples go to a party (So 20 people in total). Each of the 20 people...

10 couples go to a party (So 20 people in total). Each of the 20 people are randomly seated at a large round table with 20 chairs. Let Xi = 1, for i = 1, 2, . . . , 20, if the i th person is sitting next to the other person in their couple, and 0 otherwise. Let Y be the total number of people who are seated next to their partner. (Note that the Xi ’s all...

1. Prove that it is impossible to have a group of nine people at a party...

1. Prove that it is impossible to have a group of nine people at a party such that each one knows exactly five others in the group. 2. Let G be a graph with n vertices, t of which have degree k and the others have degree k+1. Prove that t = (k+1)n - 2e, where e is the number of edges in G. 3. Let G be a k-regular graph, where k is an odd number. Prove that the...

A group of college students want to have a party. They need to decide if they...

A group of college students want to have a party. They need to decide if they want to have it at the Beach (B) or at the Park (P) or in a Warehouse (W). They were ask to list in order their 1st, 2nd, and 3rd choice of where they want to have the party. Use the following table and answer the following questions. SHOW YOUR WORK to receive full credit. 10 students 8 students 13 students 1 st choice...

A person in power has the authority and control over the people at departmental, group or...

A person in power has the authority and control over the people at departmental, group or the whole organization. In my previous job, I worked as an office secretary. The chain of command was from the Chief executive officer to other managers. However, in my case, the head of the department had the authority to delegate duties and make prompt follow up over us. One notable concern while working as an office secretary was the departmental politics and the politics...

The English Premier League has 20 teams, throughout the season, each team plays each of the...

The English Premier League has 20 teams, throughout the season, each team plays each of the other teams once at home and once away. (e.g. Everton plays Liverpool at Anfield, which is Liverpool’s home field, and Everton plays Liverpool at Goodison Park, which is Everton’s home field.) Teams are awarded 3 points for a win, 1 point for a draw, and 0 points for a loss (a) How many combinations of wins, losses, and draws are possible for a team...

Suppose that the birthdays of different people in a group of n people are independent, each...

Suppose that the birthdays of different people in a group of n people are independent, each equally likely to be on the 365 possible days. (Pretend there's no such thing as a leap day.) What's the smallest n so that it's more likely than not that someone among the n people has the same birthday as you? (You're not part of this group.)

To begin, have each person in the group try this puzzle: Take your seven-digit phone number...

To begin, have each person in the group try this puzzle: Take your seven-digit phone number and enter the first three digits on your calculator. Multiply this number by 80. Add 1 to the product. Multiply this sum by 250. Add the last four digits of your phone number to this result. Add the last four digits of your phone number again. Divide this value by 2. Subtract 125 from this number. The result should be your seven-digit phone number....

Each person in the group will be responsible for rewriting the code to solve one of...

Each person in the group will be responsible for rewriting the code to solve one of the original parts (Alphabetizing 5 words, pig latin, reversing letters, celebrity names), without using arrays or loops. The purpose of this assignment is to practice Strings manipulation and String methods so full credit will only be given if you are utilizing the code for Strings (substring, charAt, compareTo, equals, etc). Within the group, you cannot work on the same program so only one person...

Suppose 4 people each start with $10. In each of 2 periods, each person flips a...

Suppose 4 people each start with $10. In each of 2 periods, each person flips a coin (50% probability of heads or tails). a. Suppose that each time a person flips heads, their wealth increases by 70%. If they flip tails, their wealth decreases by 30%. On average, what fraction (or percentage) of the total wealth would you expect the richest person to have in each period? (Show how you calculated the answer.) (1 pt) b. Now, repeat the exercise...

In a group of 40 people, how many cases that two or more people have the...

In a group of 40 people, how many cases that two or more people have the same birthday? NOT probability, cases please.