The Cat in the...Drawer?

Let me begin by saying, if you are ever presented with the "Cats and Socks" probability math problem...do not, I repeat, do NOT overthink it!

This story begins with my professor handing out our homework. As she was doing this, she began to explain how she knew that we were going to overthink this assignment. She urged us not to. She reminded us to take time to read the problem, and to just think on it for a while. We all agreed, of course, and class was dismissed.

After reading the problem carefully, which I actually always do, I began going through the first steps of the problem solving template. No problem, easy-peasy. I confidently jotted down my Goal, Givens, Strategy, and Conjecture (reference the photo below if you require clarification on what these are). As I tackled my Solution pathway, I immediately thought, "Ah, the probability tree diagram like we did in class!" I began sketching out my visual, carefully adding each branch's probability as I went, and of course making sure each draw's total probability equaled 1. As my tree began to become the size of a Redwood tree, my professor's voice rang in my head..."don't overthink it." Still, I was sure this was how to solve it. How else could I??

When I finished my tree, I was glad that I had persisted because it was going to make it SO much easier for me to solve the problem. This is when it hit me like a ton of bricks. I had just spent at least 30 minutes drawing my tree diagram, and now who knew how long it was going to take me to figure out the probability of every single one of these outcomes - no words.

This is when I emailed my professor crying for help; I was in too deep, and needed a lifesaver.

Now for your amusement; I attach a picture of my beautiful, yet useless, tree diagram:

 

photo and work by me

Unfortunately for me, my professor's email response never came (we later discovered it was sent but got stock in queue - lucky me). What made matters worse is that with the help of not one, but two tutors from the tutor center, we continued to overthink this. I am not even going into how...

Now for the amusing part. As I sat crying in my milk about this problem before Math class, a classmate joined me at my table. We began chatting about this problem, and within a few minutes I stopped short. My mouth dropped open - the light bulb had finally gone on. Just talking to her about it, out loud, made me realize why my professor said, "DO NOT OVERTHINK THIS." It was so simple!!

If I had only stopped and thought about what I had written as my prediction, I would have saved myself a LOT of time, work, and stress. Bottom line:

You have 12 socks total. There are only 3 colors to choose from, but you have to pull 4 out. What is the probability that you will pull 2 of the same color? 100%! If you only have 3 colors, there is no way to pull 4 without duplicating at least one color!

Sigh...I know - duh.

Well, at least I had some great practice in drawing a tree diagram. With that said, I will leave you with a website I found that has a pretty simple explanation about Probability Tree Diagrams. Enjoy!

-Amanda