# Jeremiah Fitzgerald Problem Set 3.docx - DAT 520 Problem...

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DAT 520 Problem Set 3Cumulative and Conditional ProbabilityOverview:The last problem set in Module Two exposed you to dependent trials that caused theprobability to shift slightly with each choice of sock from the drawer. Kind of sneaky, eh? This problemset gets you a little further into conditional probability with a direct look at Bayes’ theorem. Since this isa course in decision analysis and not a course in probability, we are going to introduce these concepts,use them once or twice by hand, but then let R and Excel do the heavy lifting for us the rest of the time.This problem set, however, requires hand calculations. All you should need is a calculator and your wits.Example Problem:Example 1: You are flipping a fair coin four times in total, but you are flipping it ingroups of two. In order to flip the coin for flips three and four, you have to get heads two times in a rowfor flips one and two.Problem Notes:Define success: Success for this problem is flipping a head, which isp=50%.Recall the binomial equation:Recall the Law of Total Probability equation:probability(item_1) * (item_1_%contribution) + probability(item_2) *(item_2_%contribution) + …Recall Bayes’ theorem:Questions for Example Problem:Q1: What is the probability of flipping heads four times in a row,generally?.
Q2: The way this problem is set up, what is thetotal probabilityof getting four heads?:
Let’s now call the first eventp(F1&2) and the second onep(F3&4).Next,build the table. Notice that all the % contributions have to add up to 1.Table of contributions to total probability:P% contrib.p(F1&2).25.50p(F3&4).25.50Using thelaw of total probability:

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Term
Fall
Professor
Deidre Jablonski
Tags
Probability theory
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