Frederique has 7 dogs: Molly, Ted, Fido, Rocket, Max, Sandy, and Nellie. Assume each dog is independent from the other.
a. One of the dogs has stolen her sandwich off her plate at lunch, and she wants to figure out which one. They are each equally likely to have done it, so she is going to randomly check a dog to see if he or she has bread crumbs on his or her fur. What is the probability Rocket was the one who did it?
b. What is the expected number of sandwiches that would be stolen until Rocket was the one who did it, assuming each dog is equally likely to steal her Inch, and that the sandwich thieves are working independently, from day to day (only 1 dog can steal the sandwich of the day).
c. Each time she leaves the table; there is a 0.25 chance that a dog will steal her lunch. Out of 20 lunchtimes in which she is interrupted, what is the probability that her lunch will be stolen exactly 4 times?
d. If Frederique stays at the table for the entire lunchtime, there is only a 0.0001 chance a dog will steal her lunch. Out of 10 years worth of lunches (3650) what is the approximate probability a dog will steal her lunch exactly 4 times?