Real-life systems often are composed of several components. For example, a system may consist of two components that are connected in parallel as shown in Figure 1.28. When the system's components are connected in parallel, the system works if at least one of the components is functional. The components might also be connected in series as shown in Figure 1.28. When the system's components are connected in series, the system works if all of the components are functional.

For each of the following systems, find the probability that the system is functional. Assume that component k is functional with probability Pk independent of other components.

Transcribed Image Text:

C₁ C₁ C₂ C₂ Fig.1.28 - In left figure, Components C₁ and C₂ are connected in parallel. The system is functional if at least one of the C₁ and C₂ is functional. In right figure, Components C₁ and C₂ are connected in series. The system is functional only if both C₁ and C₂ are functional.