In the automated manufacturing of computer memory chips, a company produces one defective chip for every five good chips. The defective chips (DC) have a time of failure X that obeys the PDF Fx(x DC)=(1-e^-x/2)u(x); (x in months) While the time of failure for the good chips (GC) obeys the PDF Fx(x GC)=(1-e^-x10)u(x); (x in months) The chips are visually indistinguishable. A chip is purchased. What is the probability that the chip will fail before six months of use? [Hint: Fx(x) = Σ Fx(x|A)P(A)]
