4 people running for president. There are 150 people voting, and each voter votes completely at random for exactly one person. What is the probability that at least one of them receives 30 or more votes?
4 people running for president. There are 150 people voting, and each voter votes completely at...
B. A group of 18 students cast votes for 3 candidates running for President of the group. Assume all 18 students each cast a vote for one candidate. How many different vote patterns are possible? Determine the probability that the vote pattern has exactly 2 candidates tied with the most votes. Determine the probability that one candidate gets exactly 10 votes.
4. (Voter Participation): 2 candidates A and B compete in an election. Of the n citizens, k support candidate A and the remaining (n − k) support B. Each citizen chooses whether to abstain, or to vote at a cost. A citizen who abstains receives payoff 2 if the candidate she supports wins, 1 if this candidate ties for 1st place, and 0 if the candidate loses. A citizen who votes receives the same payoffs, minus a voting cost 0...
There are 5 candidates running for student body president. There are 338 people who vote. Use the Pigeonhole Principle to determine the least number of votes a candidate could get while still winning the election?
Voters arrive at a polling booth in a remote Queensland town at an average rate of 30 per hour. There are two candidates contesting the election and the town is divided. Candidate A is far more popular, and is known that any voter will vote for her with probability 0.85. (a) The electoral officer arrived exactly 6 minutes late to open the booth, and one voter was waiting outside. What is the probability that the voter had been waiting for...
Voting records in a certain state show that 53% of those registered to vote are Democrats. In order to gather information for an upcoming story about the election, a news organization sends 9 of its reporters to choose a random registered voter to interview. The reporters are working independently, so it is possible (but unlikely) that some voter is chosen by more than one of the reporters. What is the probability that at most 6 of the 9 reporters choose...
2. Candidate H and Candidate T are both running for the same student council position. A total of 45 people vote, but each votes by flipping their own fair coin - if their coin comes up heads then a person votes for H, and if their coin comes up tails then a person votes for T. What is the probability that candidate H wins by just one vote; that is there are 23 votes for H and 22 votes for...
2. Candidate H and Candidate T are both running for the same student council position. A total of 45 people vote, but each votes by flipping their own fair coin - if their coin comes up heads then a person votes for H, and if their coin comes up tails then a person votes for T. What is the probability that candidate H wins by just one vote; that is there are 23 votes for H and 22 votes for...
4. (20 pts) Consider the study of replica voting algorithm you had done as part of the first warm-up project. For an extended analysis, Figure 4 shows the key performance results of the voting algorithms. The performance parameters are the time to deliver a data to the end-user (TTC). the number of distinet data proposals before effecting a data delivery, and the control message overhead expended to deliver a data. One of the influential parameters is the fault severity of...
n the previous two US presidential elections, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Iowa City as well, some voters complained about the long lines in some precincts, with most complaints coming from precinct A. In 2018, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with inter-arrival times that...
In a certain population, one out of 25 people are color blind, on average. (a) If a random sample of 30 people is chosen, what is the probability that there is at least one color blind person? Hint: Find the probability that none of the 30 people is color blind. (b) Use the inclusion-exclusion formula to find the probability that in a random sample of two people (i.e., the people are independently chosen), at least one of the two is...