A system consists of three identical components In order for

A system consists of three identical components. In order for the system to perform as intended, all of the components must perform. Each has the same probability of performance. If the system is to have a 0.94 probability of performing, what is the minimum probability of performing needed by each of the individual components?

Solution

Each component of the system can be understood as an independent event, then to obtain the joint probability of the entire system, which is the multiplication of all three components probabilities, we reverse the process, obtaining the cubic root of joint probability (0.94).

P(c₁)=P(c₂)=P(c₃)= ³0.94=0.98