A local euchre champion wins 78% of the games she plays. She plays 16 games in a tournament.

A. What is the probability she wins 12 or more games?

B. What is the probability she wins fewer than 8 games?

C. What is the probability she wins exactly 10 games?

A person bets 100 times on events of probability 1/100, then 200 times on events of probability 1/200, then 300 times on events of probability 1/300, then 400 times on events of probability 1/400 If the events are assumed to be independent what is the appromate distribution of the number of times the person wins?

Python

The goal of this assignment is to build a simulation of a popular children’s dice game named Beat That. Beat That is an educational game in which children learn strategic thinking and the concept of place value. While the rules of the game can be flexible, we will be playing a basic version in which 2 players (Player A and Player B) are rolling 2 dice in a 5-round game.

Game play is based on rounds. In each round, players take a turn in which they roll 2 dice. After rolling the dice, the player decides how to use the two dice values to form a 2-digit number. The goal is to arrange the digits so that they form the highest number possible. Since you are developing your computer programming skills rather than your number literacy skills, your program will automatically make the choice for the player – choosing the highest of the two possible combinations as the player’s number choice for that round. In choosing for the player in this manner you are simulating the play of expert player of Beat That rather than simulating the play of a novice.

At the close of the round, your program will compare players’ number choices for that round to determine the round scoring. The player with the highest number choice wins the round. There are 3 possible scoring outcomes of a round:

• The Players Tie this Round • Player A Wins this Round • Player B Wins this Round

The program will print a message to announce the outcome of the round.

The player who wins a round scores 1 point in the overall game. The player who loses the round does not score a point in the overall game.   If the players are tied for the round, then neither player scores a point in the overall game.

When 5 rounds have been played, the program will determine the outcome of the overall game based upon points earned. There are 3 possible outcomes of a game:

• The Players Tie the Game • Player A Wins the Game • Player B Wins the Game

The python program will print a message to announce the outcome of the game. Based upon the description above, the program should implement the functionality for playing a 5-round game of Beat That.  

When coding and testing this program, follow the approach that I take in the second part of the tutorial video where I design and build a program that simulates a multi-round Coin Toss game.

When this program is run, the console session should look like this:
Playing round 1 of Beat That... Player A rolls (2, 1) Player A chooses 21 Player B rolls (5, 2) Player B chooses 52 Player B Wins This Round!
Playing round 2 of Beat That... Player A rolls (2, 2) Player A chooses 22 Player B rolls (1, 5) Player B chooses 51 Player B Wins This Round!
Playing round 3 of Beat That... Player A rolls (4, 2) Player A chooses 42 Player B rolls (6, 1) Player B chooses 61 Player B Wins This Round!
Playing round 4 of Beat That... Player A rolls (6, 4) Player A chooses 64 Player B rolls (4, 2) Player B chooses 42 Player A Wins This Round!
Playing round 5 of Beat That... Player A rolls (2, 5) Player A chooses 52 Player B rolls (1, 5) Player B chooses 51 Player A Wins This Round!

7
Game score: Player A has won 2 rounds. Player B has won 3 rounds. Player B Wins This Game!
Before finishing your work . Please remember to apply refactoring and retesting steps

Need this in C#. Below is my code for Problem 3 of Assignment 2. Just have to add the below requirement of calculating the expected winning probability of VCU.

Revisit the program you developed for Problem 3 of Assignment 2. Now your program must calculate the expected winning probability of VCU through simulation. Run the simulation 10,000 times (i.e., play the games 10,000 times) and count the number of wins by VCU. And then, calculate the winning probability by using the following formula. The expected winning probability = the number of wins by vcu / 10,000

using System;

namespace Assignment2Problem3
{
class Program
{
static void Main(string[] args)
{
int scoreUVA= 0;
int scoreVCU=0;
int winsUVA=0;
int winsVCU=0;
Random ranGen = new Random();

Console.WriteLine("---- NCAA Basketball Game Simulator ----");

Console.WriteLine("Please enter any key to start");

Console.ReadKey();

for (int i = 1; i <= 3; i++)
{
  

scoreVCU= ranGen.Next(75, 105);
scoreUVA= ranGen.Next(65, 115);

if(scoreVCU >= scoreUVA)
{
winsVCU++;
  
  
}
else
{
winsUVA++;
}

Console.WriteLine("Game" + i + " result : VCU(" + winsVCU + ") " + scoreVCU + " - " + scoreUVA + " UVA(" + winsUVA + ")");

if (winsVCU==3|| winsUVA ==3)
{
i = 12;
}
  

}
if(winsVCU == 3)
{
Console.WriteLine("VCU wins!");
}
else
{
Console.WriteLine("UVA wins!");
}
}
}
}

(URGENCY!!) In a volleyball game between two teams , A and B, the game will be over if a team wins two out of three sets. In any set, team A has a 60 percent chance of winning the sets.
(You may use a computer to calculate the inverse matrix. All other calculations must in in your answer page)

a.   Model this game as a Markov chain. Hint: Use (WA, WB) as the states where WA is the number of sets A wins and WB is the number of sets B wins. For example state (1,0) means A won 1 set and B won 0 set. Of course, the game starts with a state of (0,0).
b.   Identify each state of this markov chain.
c.   Compute the expected number of sets before team A can win the game.
d.   Compute the expected number of sets before team B can win the game.
e.   Compute the probability that team A can win the game.
f.   Compute the probability that team B can win the game.

(URGENCY!!) In a volleyball game between two teams , A and B, the game will be over if a team wins two out of three sets. In any set, team A has a 60 percent chance of winning the sets.
(You may use a computer to calculate the inverse matrix. All other calculations must in in your answer page)

a.   Model this game as a Markov chain. Hint: Use (WA, WB) as the states where WA is the number of sets A wins and WB is the number of sets B wins. For example state (1,0) means A won 1 set and B won 0 set. Of course, the game starts with a state of (0,0).
b.   Identify each state of this markov chain.
c.   Compute the expected number of sets before team A can win the game.
d.   Compute the expected number of sets before team B can win the game.
e.   Compute the probability that team A can win the game.
f.   Compute the probability that team B can win the game.

You have $1,000 to invest and are considering buying some combination of the shares of two companies, DonkeyInc and ElephantInc. Shares of DonkeyInc will pay a return of 10 percent if the Democrats are elected, an event you believe to have a 40 percent probability; otherwise the shares pay a zero return. Shares of ElephantInc will pay 8 percent if the Republicans are elected (a probability of 60 percent), zero otherwise. Either the Democrats or the Republicans will be elected.

Instructions: Enter your response as percentage rounded to one decimal place.

a. If your only concern is maximizing your average expected return, with no regard for risk, you should invest your $1,000 in  (Click to select)  DonkeyInc.  ElephantInc.  and your expected return will be  %.

b. What is your expected return if you invest $500 in each stock? (Hint: Consider what your return will be if the Democrats win and if the Republicans win, then weight each outcome by the probability that event occurs.)

Instructions: Enter your response as percentage rounded to two decimal places.

Expected rate of return:    %


c. The strategy of investing $500 in each stock does not give the highest possible average expected return. You would:

multiple choice 2

• choose it anyway because the lower return is compensated by this strategy being less risky, as you receive a reasonable return no matter which party wins.

• not choose it because a less risky strategy cannot compensate for a lower expected return.

• choose it anyway because this strategy guarantees the same return regardless of which party wins.

• not choose it because you should always choose the strategy with the highest average expected return.

d.  Devise an investment strategy that is riskless, that is, one in which the return on your $1,000 does not depend at all on which party wins.

Instructions: Enter your responses rounded to two decimal places.

You should invest $  in ElephantInc and $  in DonkeyInc.

e. Using the investment strategy devised in part d, you will earn  % regardless of which part wins.

A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population of all people who ride this elevator have a mean weight of 160 pounds with a standard deviation of 25 pounds. If 35 of these people board the elevator, what is the probability that their combined weight will exceed 6000 pounds? Assume that the 35 people constitute a random sample from the population.

Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season. a. At the .05 significance level, can we conclude that there is a difference in the mean salary of teams in the American League versus teams in the National League? b. At the .05 significance level, can we conclude that there is a difference in the mean home attendance of teams in the American League versus teams in the National League? c. Compute the mean and the standard deviation of the number of wins for the 10 teams with the highest salaries. Do the same for the 10 teams with the lowest salaries. At the .05 significance level, is there a difference in the mean number of wins for the two groups? At the .05 significance level, is there a difference in the mean attendance for the two groups?