An assembly of four components works if at least one of its

An assembly of four components works if at least one of its four components works (components in parallel). If each component has a reliability of 0.97 and the components operate independently, what is the probability that the assembly works?

Solution

Probability that each component works =0.97

Probability that the parallel configuration sysytem works = 1 - Probability that none of the components work or the system fails

                                                                                  = 1 - 0.03⁴

                                                                                                              ^{= 0.9999 ( i.e. option D)}