Answer to Question #298728 in Statistics and Probability for Travisonny

Question #298728

One of the city's professional football teams (team 1) plays at home and another (team 2) plays away on the same night. A professional football a 0.641 probability of winning a home game and a 0.462 probability of winning an away game. Historically, when both teams play on the same night, the chance that the next morning's leading sports story will be about the team 1 is 60 percent and the chance that it will be about the team 2 game is 40 percent. Suppose that on the morning after these games the newspaper's leading sports story begins with the headline ' we win!! ' what is the probability that the story is about team 1?

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Expert's answer
2022-02-17T13:19:28-0500

Given

P(A)=0.641,P(B)=0.462,P(A)=0.641, P(B)=0.462,

P(NewsA)=0.6,P(NewsB)=0.6P(News|A)=0.6, P(News|B)=0.6

By Bayes' Theorem


P(ANews)=P(NewsA)P(A)P(NewsA)P(A)+P(NewsB)P(B)P(A|News)=\dfrac{P(News|A)P(A)}{P(News|A)P(A)+P(News|B)P(B)}

=0.6(0.641)0.6(0.641)+0.4(0.462)0.675=\dfrac{0.6(0.641)}{0.6(0.641)+0.4(0.462)}\approx0.675



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