Basic Statistics20805 marksNumerical: probability of union eventsBasic probability concepts and rules
The probability that an integrated circuit chip will have defective etching is 0.12, the probability that it will have crack defect is 0.29, and the probability that it has both defects is 0.07. What is the probability that a newly manufactured chip will have either an etching or crack defect.
The probability that an integrated circuit chip will have defective etching is 0.12, the probability that it will have crack defect is 0.29, and the probability that it has both defects is 0.07. What is the probability that a newly manufactured chip will have either an etching or crack defect. [5]
- P(Etching defect) = P(E) = 0.12 - P(Crack defect) = P(C) = 0.29 - P(Both defects) = P(E ∩ C) = 0.07 - Required: P(E ∪ C) Addition Rule of Probability: $$P(E \cup C) = P(E) + P(C) - P(E \cap C)$$ Substituting: $$P(E \cup C) = 0.12 + 0.29 - 0.07$$ $$P(E \cup C) = 0.41 - 0.07 = 0.34$$ The probabil...