1.Tracy and I spent a fair bit of time at the cottage in the summer.Unfortunately, just as we were leaving for four months, a group of five mice moved into our house.The good news is, apparently, none of the mice were pregnant when they moved in; the bad news is that mice start mating at about 6 weeks of age, a single female mouse averages about seven pups[1] per litter[2] and can have six litters per year.I also discovered that a mouse has a life expectancy of about twelve months outside and two and a half years inside a house.

(Hint: This problem is the most forward-opaque and backwards-transparent problem I have ever written.Make sure you are satisfied with your conceptual approach before starting with the math.)

a.Assuming none of the mice meet an untimely end, what is the probability that I will have more than five mice at the end of the summer?

b.What assumptions, if any, did you need to make to solve this problem?

[1] A baby mouse is called a pup.

[2] When a mouse gives birth, the cohort of pups is called a litter.