Question

In: Statistics and Probability

A group of 5 people are to be chosen from a collection of 12 people. Of...

A group of 5 people are to be chosen from a collection of 12 people. Of those of those 12: 6 Democrats, 4 Republicans, and 2 Independents.
A) How many committess are possible?
B) How many committes consist of 2 Democrats, 2 Republicans, and 1 Independent?
C) If members of the committee are chosen randomly, what is the probability that the committee consists of 2 Democrats, 2 Republicans, and 1 Independent?
D) How many committees consist of at least 4 Democrats?

Solutions

Expert Solution

Given

Total number of people = 12

Number of Democrats = 6

Number of Republicans = 4

Number of  Independents = 2

Number of people to be chosen = 5

A)

The possible number of committes

= 792 ways

B)

The possible number of committes consist of 2 Democrats, 2 Republicans, and 1 Independent

= 180 ways

C)

From above,

The possible number of committes chosen ( chosen 5 people from a collection of 12 people)= 792 ways

The possible number of committes consist of 2 Democrats, 2 Republicans, and 1 Independent = 180 ways

Now,

the probability that the committee consists of 2 Democrats, 2 Republicans, and 1 Independent = 180 / 792 = 0.2273

D)

Possible Committee:

i) 4 Democrats, 1 Republicans

ii) 4 Democrats, 1 Independent

iii) 5 Democrats

Now,

The possible number of committees that consist of at least 4 Democrats

= 96 ways


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