I have a question that unfortunately the book is not on thecramster. This questi

Question

I have a question that unfortunately the book is not on thecramster. This question is from Probability and Statisticsfor Engineers and Scientists 8th edition. The question is LetA be the event that the component fails a particular test and B bethe event that the component displays strain but does not actuallyfail. Event A occurs with probability 0.20 and event B occurswith probability 0.35.

a)What is the probability that the component does not fail thetest?
b) What is the probability that a component works perfectlywell(i.e., displays strain nor fails the test)?
c)What is the probability that the component either fails or showsstrain in the test?
I would really appreciate it if someone could help me with thisproblem thanks

Explanation / Answer

A - Fail NotA - Pass B - Strain P(A) = 0.2 I'm having some trouble understanding the language used in thequestion. If "B be the event that the component displaysstrain but does not actually fail" means "of all the parts theprobability that a part passes and strains" then: P(NotAB) = P(B) = 0.3 However, if it means "of the parts that pass, 30% strain" then: P(B|NotA) = 0.3; then: P(B|NotA) = P(BNotA)/P(NotA) P(BNotA) = P(B) = 0.3 * 0.8 = 0.24 My interpretation is the first, but use your judgment on that! (a) P(Pass) = P(NotA) = 1 - P(A) = 0.8 (b) P(Pass and no strain) = P(NotA NotB) = 0.8 - 0.3 =0.5 [or 0.56] (c) P(Strain or Fail) = P(B) + P(A) = 0.3 + 0.2 = 0.5 [or 0.44] = 1- P(NotA NotB)

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