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A Senate committee consists of 5 Republicans, 6 Democrats, and 2 Independents. A subcommittee of 3 members is randomly chosen. What is the probability that the subcommittee consists of 1 Republican, 1 Democrat, and 1 Independent?

Guest Oct 11, 2018

Best Answer 

 #1
avatar+3188 
+2

This is a multivariate hypergeometric distribution.

 

\(P[\{R,D,I\}] = \dfrac{\dbinom{5}{1}\dbinom{6}{1}\dbinom{2}{1}}{\dbinom{13}{3}}=\dfrac{30}{143}\)

Rom  Oct 11, 2018
edited by Rom  Oct 11, 2018
edited by Rom  Oct 11, 2018
 #1
avatar+3188 
+2
Best Answer

This is a multivariate hypergeometric distribution.

 

\(P[\{R,D,I\}] = \dfrac{\dbinom{5}{1}\dbinom{6}{1}\dbinom{2}{1}}{\dbinom{13}{3}}=\dfrac{30}{143}\)

Rom  Oct 11, 2018
edited by Rom  Oct 11, 2018
edited by Rom  Oct 11, 2018

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