Question

World Series. The World series is baseball is won by the first team to win four games (ignoring the 1903 and 1919 - 1921 world series, when it was a best of nine) Thus it takes at least four games and no more than seven games to establish a winner. From the document World series History on the baseball Almanac website as of November 2013, the lengths of the world series are as given in the following table.

For one of these series selected at random, let

A = event that world series was decided in four games.

B = event that world series was decided in less than six games.

C = event that world series was decided in seven games.

Describe the following events in words, and determine the number of outcome (World series) that constitute each event.

Part (a) (not A)

Part (b) (A & B)

Part (c) (A or B)

Part (d) (A & C)

Short answer

Part (a) Number of outcomes$=84$

Part (b) Number of outcomes$=21$

Part (c) Number of outcomes$=57$

Part (d) Number of outcomes$=0$

Step-by-step solution

Part (a) Step 1. Given information.

The lengths of the World Series are listed in the table below:

Games required	Frequency
4	21
5	24
6	24
7	36

A = event that world series was decided in four games.

B = event that world series was decided in less than six games.

C = event that world series was decided in seven games.

Part (a) Step 2.  In words, the event (not A) and the number of outcomes that make up the event.

The event (not A) in which the world series was determined in more than four games.

Number of outcome

$$\begin{gathered} (notA)=24+24+36 \\ (notA)=84 \end{gathered}$$

Part (b) Step 1. Given information.

The lengths of the World Series are listed in the table below:

Games required	Frequency
4	21
5	24
6	24
7	36

A = event that world series was decided in four games.

B = event that world series was decided in less than six games.

C = event that world series was decided in seven games.

Part (b) Step 2.  In words, the event (A & B) and the number of outcomes that make up the event.

The event (A & B) is when the World Series was determined in four games.

Number of outcome$(A\&B)=21$

Part (c) Step 1. Given information.

The lengths of the World Series are listed in the table below:

Games required	Frequency
4	21
5	24
6	24
7	36

A = event that world series was decided in four games.

B = event that world series was decided in less than six games.

C = event that world series was decided in seven games.

Part (c) Step 2.  In words, the event (A or C) and the number of outcomes that make up the event.

The event (A or C) is when the World Series is decided in four or seven games.

Number of outcome

$$\begin{gathered} (AorC)=21+36 \\ (AorC)=57 \end{gathered}$$

Part (d) Step 1. Given information.

The lengths of the World Series are listed in the table below:

Games required	Frequency
4	21
5	24
6	24
7	36

A = event that world series was decided in four games.

B = event that world series was decided in less than six games.

C = event that world series was decided in seven games.

Part (d) Step 2.  In words, the event (A & C) and the number of outcomes that make up the event.

The null event is (A or C). They have nothing in common in terms of consequences.

$(A\&C)=0$