Paragraph series, so four to seven games are played. (If one team wins the first

Question

Paragraph series, so four to seven games are played. (If one team wins the first four games, they have won the series, so the last three games are not played, etc.) It is believed that the team playing on their home field has an advantage because the field is familiar and their fans give them a boost As a result, the first two games are held on one competitor's home field, the next three on the opponent's field, and the last two (if needed) at the first team's field. Styles 1. The file BaseballHometeamAdvantage xlax contains the results of the World Series for the years 1922-1992. Use = COUNTIF (described in the box above) to fill in the table: American League wins at home National League wins at home American League wins away National League wins away 124 82 103 107 2. Use the data in the table to calculate P(Am winlAm home) and P(Am homelAm win). P(Am win Am home)-l Are the two probabilities found in #2 the same or different? Why? Respond by answering these questions (a) Explain in words what P(Am winlAm home) means. b) Explain in words what P(Am home lAm win) means

Explanation / Answer

The question will be clear if you make two way table based on the table

P(Am win | Am home)

Since it is given that American league home, to calculate probability of Am win, we need to consider only first column of the above table.

P(Am win | Am home)=124/206=0.6019

P(Am Home | Am win)

Since it is given that American league won, to calculate probability of Am home, we need to consider only first row of the above table.

P(Am Home | Am win)=124/227=0.5463

3) P(Am win | Am Home) means the probability of American League wins given that it was Home game for American League. Thus it gives the winning probabilities in home games.

P(Am Home | Am Win) means the probability of American League Home game given that, American league wins. Thus it gives the probability of game held at home in winning games.

These two probabilities are not equal.

But P(Am win |Am Home)/P(Am Home) = P(Am Home |Am win)/P(Am win) =P(Am win and Am Home)=124/416

which is the bayesian formula.

Home Away Total American League wins 124 103 227 National League wins 82 107 189 Total 206 210 416

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