Problem Solving

beat_gmat_09 wrote:Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games?

(A) 12.5%
(B) 25%
(C) 31.25%
(D) 68.75%
(E) 75%

Pls explain.

GMATGuruNY wrote:

beat_gmat_09 wrote:Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games?

(A) 12.5%
(B) 25%
(C) 31.25%
(D) 68.75%
(E) 75%

Pls explain.

In a best-of-seven series, at most 7 games will be played. Thus:

P(fewer than 7 games) + P(exactly 7 games) = 1

So P(fewer than 7 games) = 1 - P(exactly 7 games).

To determine P(exactly 7 games), let's say that the teams playing are team A and team B. The problem implies that each team has an equal chance of winning a game. The only way that 7 games will be played is if A wins 3 of the first 6 games and B wins the other 3.

P(AAABBB) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64
The number of ways to arrange AAABBB = 6!(3!*3!) = 20
Multiplying, we see that:
P(each team wins 3 of the first 6 games) = 1/64 * 20 = 5/16.
Thus, P(exactly 7 games) = 5/16.

So P(fewer than 7 games) = 1 - 5/16 = 11/16 = 68.75%.

The correct answer is D.

GMATGuruNY wrote: In a best-of-seven series, at most 7 games will be played. Thus:

P(fewer than 7 games) + P(exactly 7 games) = 1

So P(fewer than 7 games) = 1 - P(exactly 7 games).

goyalsau wrote:

GMATGuruNY wrote: In a best-of-seven series, at most 7 games will be played. Thus:

P(fewer than 7 games) + P(exactly 7 games) = 1

So P(fewer than 7 games) = 1 - P(exactly 7 games).

Can you please explain it a bit further,

1 = all the cases that are possible, ,

IF we try to do it like this There are two means A and B,


LIKE A team won first 4 maches, ( ONE CASE )

A team won First 4 matches out of 5 matches, { !5/ !4 = 5 ways, }

A team won first 4 matches out of 6 matches { !6/!4 * !2 = 15 ways }

Now i am not getting the answer,

I m not to understand that this particular line

P(fewer than 7 games) + P(exactly 7 games) = 1

IM_onthegrind wrote:Hi Guru, everything makes perfect sense in your explanation, but I don't understand one thing. What happened to the 7th game? You never accounted for that. Why is that?

Thanks!