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shepuryov [24]
3 years ago
9

A city council consists of six democrats and five republicans. If a committee of seven people is selected, find the probability

of selecting four Democrats and three republicans.
Mathematics
1 answer:
Mamont248 [21]3 years ago
7 0
Use hypergeometric distribution where there are two categories of identical objects/persons, each with a know size.
d=number of Democrats selected
D=total number of Democrats = 6
r=number of Republicans
R=total number of Republicans =5
Then 
P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}
where 
C(n,r)=\frac{n!}{(n!(n-r)!)}  = combination of r items selected from n,
D+R=total number of members = 6+5 =11
d+r=number of members selected = 7

P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}
P(4,3)=\frac{C(6,4)C(5,3)}{C(6+5,4+3)}
=\frac{C(6,4)C(5,3)}{C(11,7)}
=\frac{15*10}{330}
=\frac{5}{11}

Answer: the probability of selecting 4 Democrats and 3 Republicans is 5/11

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