Question $1$

a$)$ A system has $25$ components in series. Each component has a reliability of $0\mathrm{.}99.$ What is the reliability of the system?

b$)$ A product has four components A$,$ B$,$ C$,$ and D$.$ The finished product must have a reliability of $.95.$ The first three components come from a supplier, and have reliabilities of $\mathrm{.}99,\mathrm{.}98,$ and $\mathrm{.}995.$ The fourth component is being designed now. What must the reliability of component $D$ be in order to meet the product reliability condition?

c$)$ Which product design below has the higher system reliability?