WILL WARD

Warning: Spoilers Follow The Question If you roll a single die six times, what is the probability of a number being rolled more than once? Answer There are six sides to a die, each side representing a unique number. A series of six rolls where no number is repeated could be 1, 2, 3, 4, 5, 6 or 5, 4, 3, 2, 1, 6 In fact there are 6! permutations of roll sequences where no number is repeated. And, there are possible roll sequences including ones with no repeats and ones with them. With this we can calculate the probability of rolling a sequence with no repeats: This means the probability of a repeated number in a sequence of six rolls is

Warning: Spoilers Follow Ex 2.14: Consider the following scenario, from Tversky and Kahneman: Let A be the event that before the end of next year, Peter will have installed a burglar alarm system in his home. Let B denote the event that Peter's home will be burglarized before the end of next year. (a) Intuitively, which do you think is bigger, or ? Explain your intuition. We're not given any information about Peter's situation at all. Information such as whether or not Peter has considered installing a burglar alarm previously, whether or not his home has been burglarized previously, how much money Peter has to invest in an alarm, or what he stands to lose in case of a burglary; if he has…

Warning: Spoilers Follow From Unit 2 of Blitzstein/Hwang Probability (Harvard's Stat 110 probability course) Ex. 2.11 An exit poll in an election is a survey taken of voters just after they have voted. One major use of exit polls has been so that news organizations can try to figure out as soon as possible who won the election, before the votes are officially counted. This has been notoriously innacurate in various elections, sometimes because of selection bias: the sample of people who are invited to and agree to participate in the survey may not be similar enough to the overall population of voters. Consider an election with two candidates, Candidate A and Candidate B. Every voter is…