The figure shown above is a schematic representation of a system comprised of three components.

The system operates properly only if all three components operate properly. The three components are said to operate in series. The components could be mechanical or electrical; they could be work stations in an assembly process; or they could represent the functions of three different deparlrnents in an organization. The probability or Failure for each component is listed in the table.
Assume the components operate independently of each other.
Component Probability of Failure

a. Find the probability that thc system operates properly.

b. What isthe probability that at least one of the components will fail and therefore that the system will fail?