Question 3

Scenario: In one batch of 10,000 solder joints, inspector A found 734 that were judged defective and inspector B found that 757 were judged defective. 940 of the 10,000 solder joints were judged defective by at least one of them. Consider randomly selecting one of the defective solder joints.

Events:

  • - Judged defective by inspector A.
  • - Judged defective by inspector B.

Probabilities:

  • .
  • .
  • .

(a)

Problem: What is the probability that the selected joint was judged to be defective by neither of the two inspectors?

Process: If neither inspector found it defective, that means it's not defective. So, the question is really asking what the probability is that a randomly selected solder joint is not defective. This can be found by finding the complement of .

Answer: 0.906.

Summary

For the probability of a selected object not belonging to neither nor , see the Question 1 (c) Summary.

(b)

Problem: What is the probability that the selected joint was judged to be defective by inspector B but not by inspector A?

Process: The phrase "inspector B but not ... inspector A" indicates we're only interested in the events of and the events not in . This is expressed as the intersection (and) of and the complement of .

Answer: 0.0206.

Summary

The probability of the intersection (and) of and is:

For the probability of a selected object belonging to only or only , see the Question 1 (e) Summary.