Basic Statistics20825 marksNumerical: Probability of components not failingBasic probability concepts and rules
A piece of equipment will function only when all the components A, B, and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will not fail before the end of one year?
A piece of equipment will function only when all the components A, B, and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will not fail before the end of one year? [5]
- Equipment functions only when all of A, B, C are working. - $P(A \text{ fails}) = 0.15$ - $P(B \text{ fails}) = 0.05$ - $P(C \text{ fails}) = 0.10$ - Component failures assumed independent. - Find: $P(\text{equipment does not fail in one year})$ Probability each component does NOT fail: $$P(A ...