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#1 2007-07-17 01:35:22

buzhitao
Member
Registered: 2007-07-10
Posts: 2

Just 1 Probability Problem

A team of 5 persons is to be selected from 3 lecturers and 6 students to participate in the "SuperTeam" Competition.  What is the probability that the team consists of at least 3 students ?

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#2 2007-07-17 02:18:45

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: Just 1 Probability Problem

There are (9 choose 5) ways of selecting the team.   That's 126.   

You want to know what are the chances of having 3, 4, or 5 students on the team.   You can calculate each of those cases and add them together or you can calculate the probability of only have 2 students on the team and then subtracting it from 1.

Number of different teams consistenting of 3 lecturers and 2 students: 
(3 choose 3) * (6 choose 2) = 1 * 15 = 15

So 15/126 (.119) is the probability of having 3 lectures and 2 students.   

1 - 15/126 (.881) is the probability of having 3, 4 or 5 students on the team.

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