Your home is infested with feather dusters. Your cat, Fluffy, is going to save you from this horrible peril. This puzzle is dedicated to a cat I had—Tammy—who took out a feather duster; she was so proud. On an even-numbered day (day number by calendar), there is an 80% chance that Fluffy can take out one feather duster. On an odd-numbered day, the chance is 70%. There are four feather dusters. On days when you are not quick with the kitty treats, the chance is at most one-half of the figures given. Each day, there is a 25% that Fluffy will sleep all day. The wind outside gusts to up to 50 km/h.
Two questions: 1) What is the minimum number of days it will take Fluffy to take out all of the feather dusters? 2) What is the probability of three odd-numbered days in a row?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 17, 2018> at noon Pacific Time. I will post the answer shortly after.