A sample of the parts is taken from each shift (1, 2, or 3) in a manufacturing operation to investigate the relationship between the shift and the quality of parts (conforming or nonconforming) being produced. The number of conforming and nonconforming parts per shift is summarized in the table below:
Shift 1 
Shift 2 
Shift 3 
Total 

Conforming 
370 
285 
175 
830 
Nonconforming 
30 
15 
25 
70 
Total 
400 
300 
200 
900 
What is the probability a randomly chosen part is conforming?
What is the probability a randomly chosen part is conforming or from shift 2?
What is the probability a randomly chosen part is conforming given we know the part is from shift 2?
What is the probability a randomly chosen part is from shift 2 given we know the part is conforming?
Solution:
What is the probability a randomly chosen part is conforming?
Answer: The probability of a randomly chosen part is conforming is:
What is the probability a randomly chosen part is conforming or from shift 2?
Answer: The probability a randomly chosen part is conforming or from shift 2 is:
What is the probability a randomly chosen part is conforming given we know the part is from shift 2?
Answer: The probability a randomly chosen part is conforming given we know the part is from shift 2 is:
What is the probability a randomly chosen part is from shift 2 given we know the part is conforming?
Answer: The probability a randomly chosen part is from shift 2 given we know the part is conforming is:
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