An electrical system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.90. The probability that at least one of the two components does so is 0.96. The probability that both components do so is 0.75.
a. Find the probability that the first component functions satisfactorily during its design life.
b. Do the components function independently? Explain.
c. Find the probability that the first component functions satisfactorily during its design life given that the second one does not.
d. Find the probability that neither component functions satisfactorily during their design life.
e. Find the probability that exactly one component functions satisfactorily during its design life.