Goodeating Dog Chow Company produces a variety of brands of dog chow. One of their best values is the 50-pound bag of Goodeating Dog Chow. George Hamilton, president of Goodeating, uses a very old machine to load 50 pounds of Goodeating Chow automatically into each bag. Unfortunately, because the machine is old it occasionally over-or under-fills the bags. When the machine is correctly placing 50 pounds of dog chow into each bag, there is a 0.10 probability that the machine will only put 49 pounds in each bag the following day, and there is a 0.20 probability that 51 pounds will be placed in each bag the next day. If the machine is currently placing 49 pounds of dog chow in each bag, there is a 0.30 probability that it will put 50 pounds in each bag tomorrow and a 0.20 probability that it will put 51 pounds in each bag tomorrow. In addition, if the machine is placing 51 pounds in each bag today, there is a 0.40 probability that it will place 50 pounds in each bag tomorrow and a 0.10 probability that it will place 49 pounds in each bag tomorrow.
(a) If the machine is loading 50 pounds in each bag today, what is the probability that it will be placing 50 pounds in each bag tomorrow?
(b) Resolve part (a) when the machine is only placing 49 pounds in each bag today.
(c) Resolve part (a) when the machine is placing 51 pounds in each bag today.