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On the morning of September 30,1982, the won-lost records
Chapter 3, Problem 71P(choose chapter or problem)
Problem 71P
On the morning of September 30,1982, the won-lost records of the three leading baseball teams in the Western Division of the National League were as follows:
Team |
Won |
Lost |
Atlanta Braves |
87 |
72 |
San Francisco Giants |
86 |
73 |
Los Angeles Dodgers |
86 |
73 |
Each team had 3 games remaining. All 3 of the Giants’ games were with the Dodgers, and the 3 remaining games of the Braves were against the San Diego Padres. Suppose that the outcomes of all remaining games are independent and each game is equally likely to be won by either participant. For each team, what is the probability that it will win the division title? If two teams tie for first place, they have a playoff game, which each team has an equal chance of winning.
Questions & Answers
QUESTION:
Problem 71P
On the morning of September 30,1982, the won-lost records of the three leading baseball teams in the Western Division of the National League were as follows:
Team |
Won |
Lost |
Atlanta Braves |
87 |
72 |
San Francisco Giants |
86 |
73 |
Los Angeles Dodgers |
86 |
73 |
Each team had 3 games remaining. All 3 of the Giants’ games were with the Dodgers, and the 3 remaining games of the Braves were against the San Diego Padres. Suppose that the outcomes of all remaining games are independent and each game is equally likely to be won by either participant. For each team, what is the probability that it will win the division title? If two teams tie for first place, they have a playoff game, which each team has an equal chance of winning.
ANSWER:
Step 1 of 2
Our goal is
We need to find the probability that it will win the division title.
From the given information we know that each team had 3 games remaining.
Then all three of the Giants’ games were with the Dodgers, and the three remaining games of the Braves were against the San Diego Padres.
Then the table is given below.
Team |
Won |
Lost |
Atlanta Braves |
87 |
72 |
San Francisco Giants |
86 |
73 |
Los Angeles Dodgers |
86 |
73 |