binominal problems

We’re looking for the probability that the Colonials win exactly https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?0of https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?7games chosen at random, assuming that the Colonials are equally likely to win a game as not to win it. Note that we’re not looking for the probability that the Colonials win a specific https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?0of those https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?7games, but rather for the probability that they win any https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?0of those https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?7games. What we can do is to find the probability that the Colonials win a specific group of https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?0of the https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?7games, repeat this for all possible specific groups of https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?0of the https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?7games, and then add up all these probabilities to obtain the probability that the Colonials win any https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?0of the https://secure.aleks.com/alekscgi/x/math2htgif.exe/M?7games.

 
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