Question 1167849
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A company is to hire two new employees. They have prepared a final list of
eight candidates, all of whom are equally qualified. Of these eight candidates,
five are women. 

Suppose the company decides to select two persons randomly from these eight
candidates.

a. What is the probability that:

i. At least one candidate selected is a woman?<pre>
Since 5 are women, 3 are men.  We get the probability of the complement
event and subtract from 1:
<pre>
1 - (the probability that both are men) = 1 - C(3,2)/C(8,2) = 1 - 3/28 =
28/28 - 3/28 = 25/28
</pre>b. Let X denote the number of women in this sample.

i. Write the probability distribution of X.<pre>
X                                         P(X)
----------------------------------------------     
0   [C(5,0)C(3,2)]/C(8,2) =  (1)(3)/28 =  3/28
1   [C(5,1)C(3,1)]/C(8,2) =  (5)(3)/28 = 15/28
2   [C(5,2)C(3,0)]/C(8,2) = (10)(1)/28 = 10/28

ii. Find the standard deviation of X.

x     p      x∙p     x<sup>2</sup>    x<sup>2</sup>∙p
----------------------------------------------     
0    3/28     0       0     0
1   15/28   15/28     1   15/28
2   10/28   20/28     4   40/28
-------------------------------
       E(x)=35/28   E(x<sup>2</sup>)=55/28

{{{sigma=sqrt(E(x^2)-(E(x^"")^""^"")^2)=sqrt(55/28-(35/28)^2)=0.633865691}}}


Edwin</pre>