Question

A committee of size 3 is to be selected from 6 men and 2 women. (a) Find the probability distribution of the number of women selected in the committee, and (b) Find the standard deviation. *

Answer 1

a) The probability distribution of the number of women in the committee is computed here as:

P(X = x) = Number of ways to select x women from 2 women * Number of ways to select (3 - x) men from 6 men / Total ways to select 3 members from 8 members

The probabilities are therefore computed here as:

This is the required probability distribution here.

b) The computations for standard deviation are made using the following table:

X	P(x)	xP(x)	x^2P(x)
0	0.3571	0.0000	0.0000
1	0.5357	0.5357	0.5357
2	0.1071	0.2143	0.4286
	1.0000	0.7500	0.9643

For standard deviation, we obtain the moments here as:

as seen from the third column of the table.

as seen from the last column of the table

Therefore now the standard deviation here is computed as:

Therefore 0.6339 is the required standard deviation here.