Homework 5 Conditional Probability, Reliability, and Bayes\' Theorem This homewo

Question

Homework 5 Conditional Probability, Reliability, and Bayes' Theorem This homework is based on the current NCAA Men's Basketball Championship Tournament, commonly referred to as March Madness. There are 16 teams remaining in the single elimination tournament. We are going to use these games in our analysis of conditional probability, reliability, and Bayes' Theorem. Below is the bracket for the remaining games in the tournament. For those of you who are unfamiliar with this setup, it is pretty straight forward. Wisconsin is an 8-seed and they play a 4-seeded Florida in the Sweet 16. The winner advances to the Elite 8 andplays the winner of the Baylor /South Carolina game, and so on. The seeds were used to determine the historical probability of one team beating another Seed Team National Elite 8 Final 4 Championship Champion Sweet 16 8 Wisconsin 4 Florida 3 Baylor 7 S. Carolina 1 Gonzaga 4 W. Virginia 11 Xavier 2 Arizona 1 Kansas 4 Purdue 3 Oregon 7 Michigan 1 N. Carolina 4 Butler 3 UCLA 2 Kentucky

Explanation / Answer

I. P(A and Oregon)=0.314*0.600=0.1884

II. P(Oregon|A)=P(A and Oregon)/P(A)=0.1884/0.314=0.6

III. P(B)=0.314*0.6*0.375+0.314*0.4*0.4=0.12089

IV. P(Michigan|B)=P(B and Michigan)/P(B)=(0.314*0.4*0.4)/0.12089=0.4156

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