(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two teams, A and B, play a series of games. If team A has probability .4 of

winning each game, is it to its advantage to play the best three out of five games

or the best four out of seven? Assume the outcomes of successive games are

independent.

2. Relevant equations

http://en.wikipedia.org/wiki/Binomial_distribution

vs.

http://en.wikipedia.org/wiki/Negative_binomial_distribution

3. The attempt at a solution

This problem is basically a plug and chug problem. However, I do have some difficulties interpreting this problem.

When the problem states "the best three out of five games" and "the best four out of seven games", does it mean that when Team A wins three times or four times (given the respective parameters), does the game end???

Example 1: Team A wins three times -> game is over.

Example 2: Team A wins three times -> game continues until 5 games are played.

Since a person can interpret this many ways, I decided to just write out the solution for each example.

Solution 1: Take the summation of the negative binomial distribution of 3 successes, p = 0.4, and the number of trials from i = 3 to i = 5.

Solution 2: Take the summation of the binomial distribution from i number of successes from i = 3 to i = 5, p = 0.4, and the number of trials is 5.

Assuming that if both the cases were true, is my solution or "method" for each one correct? I know that 3 out of 5 game is the correct answer; nevertheless, I am just curious at the process to reach it because many people I met have different interpretations and methods to answer this problem.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Do I Use the Binomial or the Negative Binomial?

**Physics Forums | Science Articles, Homework Help, Discussion**