A system consists of four components connected as shown in the following diagram:
Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.10, 0.05, 0.10, and 0.20, respectively, what is the probability that the system functions?
P(system functions) = P[(A ? B) 
(C D)]. Now P(A ? B) = P(A)P(B) = (1?0.10)(1 ? 0.05) = 0.855, and P(C D) = P(C) + P(D) ? P(C ? D) = (1?0.10) + (1 ? 0.20) ? (1 ? 0.10)(1 ? 0.20) = 0.98.
Therefore
P[(A ? B) ? (C D)]=P(A ? B) + P(C D) ? P[(A ? B) ? (C ?D)]
=P(A ? B) + P(C D) ? P(A ? B) P(C D)
= 0.855 + 0.98 ? (0.855)(0.98)
= 0.9971
You might also like to view...
Todos los siguientes son tipos de fusibles limitadores de corriente SALVO:
a. Clase H. b. Clase J. c. Clase L. d. Clase R.
A triangle is cut into two equal halves. The base of the whole triangle is 38 centimeters and the height is 18 centimeters. What is the area of each triangle?
Fill in the blank(s) with the appropriate word(s).
During a manicure sessions, Jimmy accidentally cuts Jenny's skin and she bleeds. Jenny says that she has AIDS. What should Jimmy do?
What will be an ideal response?
Technician A says that copper jumper cables are better than aluminum jumper cables. Technician B says that aluminum jumper cables are better than copper jumper cables. Which technician is correct?
A) Technician A only B) Technician B only C) Both technicians D) Neither technician