Question

RA Dodgers and Poston Blue Sox advance to the Country Series. A team needs to win four games to be the champion of the Country Series. Maximum of seven games are played to decide the champion. During the regular season, both teams played ten games against each other, where RA Dodgers won six games and Poston Blue Sox won four games. In other words, the probability that RA Dodgers win against Poston Blue Sox is 0.6. Assume that no games end in a tie.

(a) What is the probability that RA Dodgers becomes the champion of the Country Series at the fourth game?

(b) What is the probability that RA Dodgers becomes the champion of the Country Series?

Answer 1

Given

P( RA Dodgers win against Poston Blue Sox)=0.6

a)

To find the probability that RA Dodgers become champion in 4th game that is they win all the first 4 games and the probability is given by

This is because of become champion at the 4th game they must win all the first 4 games.

b)

Let x:number of matches RA Dodgers win out of 7 matches against Poston Blue sox

Now for simplicity call this probability as p

P( RA Dodgers win against Poston Blue Sox)=0.6=p

So n=7

and they should win atleast 4 out of 7 games to become the champion so probability that they will be champion can be found out using the binomial distribution with n=7 and p=0.6

So

  

Similarly

  

So the probability that RA Dodgers become the champion is

Hence the probability is 0.710208.

Thank you !!