A certain facility produces drill bits which are made of eit…

A certain facility produces drill bits which are made of either steel, cobalt, or diamond. Suppose that 75% of the drill bits are steel, 20% are cobalt, and 5% are diamond. Further, suppose that 10% of the steel drill bits fail, 5% of the cobalt drill bits fail, and 1% of the diamond drill bits fail. What is the probability that the drill bit is cobalt and fails?   

A manufacturing facility constructs airplanes with a mean of…

A manufacturing facility constructs airplanes with a mean of 50 tons and a variance of 400. What is the smallest probability that an airplane’s weight will be between 20 tons and 80 tons? Note that we are not assuming normality.  [Hint: Use Chebyshev’s theorem.]