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Experiment Test Program Planning and Statistical Analysis Fundamentals
Published in R. E. Little, D. M. Kosikowski, Mechanical Reliability Improvement, 2002
R. E. Little, D. M. Kosikowski
Two fundamental probability concepts are illustrated in this classical fair-coin experiment test program example. First, the probabilities of occurrence for independent outcomes can be multiplied to establish the probability that the corresponding collection of outcomes will occur (together), e.g., the probability of observing HH as the outcome of two independent flips is (1/2)⋅(1/2)=1/4. Second, the probabilities pertaining to a collection of mutually exclusive experiment test program outcomes can be summed to establish the probability that one of these outcomes will occur. (Note that the sum of probabilities for mutually exclusive and exhaustive outcomes is always equal to one.)
Basic Mathematics
Published in M. Modarres, What Every Engineer Should Know About Reliability and Risk Analysis, 2018
It is important to understand the concept of independent events before attempting to multiply and add probabilities. Two events are independent if the occurrence or nonoccurrence of one does not depend on or change the probability of the occurrence of the other. Mathematically, this can be shown by () Pr(E1 | E2)=Pr(E1)
Probability
Published in Lawrence S. Aft, Fundamentals of Industrial Quality Control, 2018
The probability of occurrence of both an independent event A and an independent event B is the product of their respective probabilities. Remember that occurrence or nonoccurrence of one independent event does not influence the probabilities associated with other independent events. P(Aand B)=P(A)P(B)
A note on independence in probability
Published in International Journal of Mathematical Education in Science and Technology, 2020
Intuitively, two events are considered to be independent of each other if the occurrence of one does not affect the probability of the other one occurring. Formally, two events A and B are said to be independent if and only if (Grimmett & Stirzaker, 2001; Miller, 2001). For the Venn diagram in Figure 1 this equality becomes , which may be rearranged to give the following quadratic equation in r: From this we obtain noting that in order for r to be a real number, we require q and s such that