Cricket Series Probability

[KK]

I am reframing one of the questions from the strategic guessing lab and want to know how to solve it:

In a cricket match series, two teams are playing. There are total of 8 games played. The team that wins the first 4 games wins the series. What is the probablity that less than 8 games be played in the cricket series?

Please guide me how to approach this question.

[RA]

Hi!

The probability of either team winning game-1is 1.

Now game-2,3 and 4need to be won by the team that won the first game. Probability = 1/2 * 1/2 * 1/2

Total Probability = 1 * 1/2 * 1/2 * 1/2 = 1/8.

Please confirm if this is the correct answer.

Thanks,
RA

[RonPurewal]

whoa whoa whoa.

there are at least 2 things wrong with the problem stated in the original post:

1, you first say "There are a total of 8 games played", and then immediately turn around and ask for "the probability that less than 8 games (are) played".
these can't both be true; if the first statement is literally true (8 games are played), then the foregoing probability is zero, because, well, 8 games are played.

2, i'm assuming that "wins the first 4 games" is supposed to mean "the first team to accumulate 4 wins".
if this is the case, then the probability of playing fewer than 8 games is 1, or 100%.
after seven games have been played, ONE of the teams is GUARANTEED to have accumulated at least 4 wins (the wins are either 4-3, 5-2, 6-1, or 7-0). so, if you're only playing the series until one team has four wins, then you will NEVER need to play an eighth game.

so ... what's the correct problem statement?