Worked solution · Exam P
This Exam P sample reference tests Hypergeometric Sampling. Exactly one low-risk worker means selecting one from each risk class. There are 20(5)=100 favorable pairs among C(25,2)=300, giving 1/3, choice D.
Independent solution
Setup
Every two-worker subset is equally likely under sampling without replacement.
Model
Exactly one worker from each risk class can be selected by choosing one of the 20 low-risk workers and one of the five other workers.
Compute
There are 100 favorable pairs among 300 total pairs, giving one third.
Answer
The probability of one worker from each class is one third.
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Original practice · fully worked
A plant has 18 standard workers and 7 advanced workers. Three workers are selected uniformly without replacement. Find the probability that exactly one selected worker is advanced.
There are C(7,1)C(18,2)=1071 favorable teams among C(25,3)=2300 total teams, giving 0.46565, choice D.
Setup
Every three-worker team is equally likely under sampling without replacement.
Model
A favorable team contains one of the seven advanced workers and two of the 18 standard workers.
Compute
There are 1,071 favorable teams among 2,300 total teams, giving approximately 0.465652.
Answer
The probability rounds to 0.4657.
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