Question

Major League Baseball considers the option of one team being the home team for an entire series. The World Series consists of up to seven games. The first team to win four games wins the series. Records over the past century show that there is a home field advantage; the home team has about a 55% chance of winning. How often will the team that begins at home win the series? Remember to assume that one team is always at home (which is different than how teams alternate home field). Give an example of “one” trial and its result.

What is the component to be repeated?

How will you model each component from equally likely random digits?

Answer 1

Here one game is a trial and its result is win or loss the game of a particular team.

in the above example we assume that the hometeam is a team whose winnng probability is o.55 that is probability of success of home team of each game (trial) is = 0.55

Since the probability of each trial is same for each game the trials are independent.

There are only two possible outcomes as hometeam winn the game called as success and hometeam loss the game called as failure.

If the winning probability of each team is same that is 0.5 then the trials are called equally likey.

If we denote success as 1 and failure as 0 and assume that the probabilty of success = 0.50 then 0 and 1 are are equaly likely.

Suppose X be a random variable taking value 1 when the hometeam win the game and 0 when the hometeam loss the game.

Using this random variable we can make a model of a digits.