Fussy Probability Applications

I find probability word problems to be a bit fussy. Fussy word problems make probability a tough course to pass. You say?

 

fussy: by definition, it is showing excessive or anxious concern about detail, full of unnecessary detail or decoration

I do agree with first part (concern about detail), but I do not agree with the second part (full of unnecessary detail or decoration).

Probability is traditionally considered one of the most difficult areas of mathematics, since probabilistic arguments often come up with apparently paradoxical or counterintuitive results.

The problem is that probability and statistics are often taught very formally and tightly coupled with formal terms and notation. Students can be taught what a factorial is, how to calculate the number of permutations, what a normal distribution looks like, but they will have a hard time understanding how to make use of those terms without first developing their intuition.
Most people have a very strong intuition about how to calculate probabilities, combinatorics, and statistics from a lifetime of real-world experience.

 

Sorry. I meant to say FUZZY. By fuzzy it is MEANT to be BLURRY OR UNCLEAR. I find probability to be insanely hard. I plan to study a first semester probability course after calculus.

 

We humans like two conditions: yes and no. “Maybe” is frustrating. It’s hard to deal with the reality that the whole universe is one big “maybe” and doesn’t have any “yes” or “no”.

Probability functions are easy. Probability problems are hard. They are three conditions, yes, no, or maybe. That’s when you must translate language into those functions, and this is where most students trip and fall.

So to sum up, there is more than one reason why such problems are hard: mathematics is insufficient to solve them because they require insight and patience and the solutions are counter-intuitive and therefore hard to accept. The best strategy is to take each problem slowly and map them out. Make pictures. Don’t rush. Probability offends the rational mind until it can finally give up and admit that the world is just one big probability. Then it gets a little easier.

 

I am looking forward to basic probability in the future.