Final answer:
To find the probability that an employee selected at random from administrative positions is a graduate, calculate the percentage of graduates in administrative positions out of the total in such positions. The calculation shows there is a 58.54% chance of selecting a graduate.
Step-by-step explanation:
The question involves finding the probability that an employee selected at random from those working in administrative positions will be a graduate in a company where 15% of the employees are graduates and 80% of these graduate employees are in administrative positions.
First, let's identify the percentage of graduate and non-graduate employees in administrative positions. Since 80% of the 15% of graduate employees are in administrative positions, that's 0.80 × 15% = 12%. For non-graduates, 10% of the 85% of employees are in administrative positions, which is 0.10 × 85% = 8.5%.
To find the probability of selecting a graduate employee from the administrative positions, we need to calculate the percentage of graduate employees in administrative positions out of the total percentage of employees in administrative positions. This can be calculated as follows:
Probability (Graduate | Administrative) = Number of Graduates in Administrative Positions / Total Number of Employees in Administrative Positions
Thus, Probability (Graduate | Administrative) = 12% / (12% + 8.5%) = 12% / 20.5% = 0.5854 or 58.54%
So, there is a 58.54% chance that an employee selected at random from the administrative positions is a graduate.