Lucky Charms !!

So as many of you know I am in grad school and I am almost finish. For our class this semester we had to keep track of our activities and thoughts in a blog. I wasn't trying to manage two different blogs so I'm adding some "course work" to this one :) 

Our first assignment was the following Lucky Charms problem: 

Setting. Lucky Charms® has a "Toy Story" promotion. Inside each box is one of five figures from the movie "Toy Story": Woody, Buzz Lightyear, Rex, Hamm, or Green Army Man. You want to collect all five of these toys for your child, who loves "Toy Story."

Problem. How many boxes of Lucky Charms® will you have to buy?

Conducting a Simulation. Since we do not want to buy the boxes of Lucky Charms®, we will use a simulation. However, the set-up for the simulation is up to you. Will you use a die, a random number generator, a spinner, draws from a hat, etc. to conduct your simulation? How many times should you run the simulation, given that you could imagine one person buying many fewer boxes than another person in an attempt to collect all five prizes. In the space below, create a system for simulating the prizes coming from a box of cereal. Be sure to note any assumptions made.

How many times do you plan to run the simulation?

I ran the simulation 10 different times using a random number generator. 

What assumptions did you make in setting up the simulation?

I assumed that one number would occur more often than others. 

How many boxes of cereal should someone buy to have a good chance of getting all five prizes? How did you arrive at this number?

A person should have to buy around 11 boxes of cereal to have a good change of getting all the prizes. I ran the simulation 10 times and each time recorded the amount of "buys" it took to get all 5 prizes. I then took an average of the 10 simulations and arrived at 11. 

Do you believe you have enough data to make a sound conclusion? What if you compiled results from everyone in class? 

I do not feel like my 10 simulations are enough to make a sound conclusion. However, if we complied results from everyone in the class and took the average we would have a better idea of an "ideal number" of boxes to purchase.