Answer:
(a) The proportion of qualified anglo candidates hired is 96.6%.
(b) The proportion of qualified persons of color candidates hired is 85.7%.
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%.