Raising the bar

Chapter 4. Probability

Unit 4.9. Problem solving strategy

1. Make sure that you solve at least two typical exercises from each section of Chapter 3 in NCT.
2. Some exercises are easier than they look. This is where writing down all the relevant equations is particularly useful. Remember what you need to find. In general, to find $latex n$ unknowns it is sufficient to have $latex n$ equations involving them. One of my students was able to solve those exercises without any knowledge of conditional and joint probabilities, just using common sense and the percentage interpretation of probabilities.
3. To write down the conditions, you need a good notation. Avoid abstract notation and use something that reminds you of what you are dealing with, like $latex A$ for Anthropology class.
4. When looking for a solution of a problem, write down all the relevant theoretical facts. Don't limit yourself to conclusions; repeat everything with proofs and derivations. Omit only what is easy; after a while everything will become easy. If you still don't see the solution, go back by one or two steps and solve simpler similar exercises.
5. When you clearly see the idea, don't calculate the numbers. Learn to save your time by concentrating on ideas.
6. If section exercises are too simple, don't waste your time and go directly to end-of-chapter exercises.
7. Everybody finds difficult exercises that require orderings and combinations. Solve more of them, until you feel comfortable. However, it's not a good idea to solve all of them. Combinatorics is a very narrow area of statistics.

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