Amanager (who happens to be a white anglo) is responsible for hiring personnel in her department. she is accurate 95% of the time in assessing the qualifications of white anglo candidates (that is, 95% of the candidates who are qualified she assesses as qualified and 95% of the candidates who are unqualified she assesses as unqualified). she is accurate only 80% of the time for candidates of color. she hires candidates (they then become employees) that she assesses as qualified. in the pool of candidates, 60% of white anglo candidates and 60% of candidates of color are qualified.(1) what proportion of white agnlo hirees are qualified? (2) what proportion of the person of color who are hired are qualified?

(a) The proportion of qualified anglo candidates hired is 96.6%.

(b) The proportion of qualified persons of color candidates hired is 85.7%.

Step-by-step explanation:

For the anglo candidates, the manager will hire two groups:

Group 1: the ones that are qualified and she assess correctly

Group 2: the ones that are not qualified but she does not assess correctly

If we consider a group of 100 Anglo candidates, 60 are qualified. The probability that they are in the Group 1 is:

The probability of being in Group 2 is

The proportion of qualified anglo candidates hired is equal to the probability of being in Group 1, over the sum of the probabilities of being in Group 1 and 2:

The proportion of qualified anglo candidates hired is 96.6%.

For the people of color is the same analysis, but the probabilities of assessment are different.

Group 1: the ones that are qualified and she assess correctly

Group 2: the ones that are not qualified but she does not assess correctly

If we consider a group of 100 non-Anglo candidates, 60 are qualified. The probability that they are in the Group 1 is:

The probability of being in Group 2 is

The proportion of qualified anglo candidates hired is equal to the probability of being in Group 1, over the sum of the probabilities of being in Group 1 and 2:

The proportion of qualified persons of color candidates hired is 85.7%.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!