Wow! What a crazy week. At one point or another I've covered every aspect of probability at some point in K-12, but I've never done them all at once in one week. This week I was introduced to a few concepts I hadn't seen before, the first was the idea of the "fair game". This concept basically looks at games of chance and compares the cost of playing the game to the payoff of each game. If the payoff is equal to the buy-in the game is considered fair. I wish I would have known this about 15 years ago when I turned 18 and went to a casino for the first time. Those games would not be considered "fair" by a long shot.
A concept I struggled with this week was the idea of permutation versus combination. It's actually a pretty simple concept, permutation is a data set in which the order of the elements is specific, whereas combination is the same idea except the order doesn't matter. For some reason I really struggled figuring out when to use the correct algorithm to solve each type of problem. The question I missed on last weeks test was about home builders with 6 lots to build but 12 model's to choose from that they could build. I solved it as a permutation, but of course it was a simple combination. My answer was only off by about 650,000 but I still got it wrong, talk about nitpicking. Check out this great video on permutations!
I really like statistics, one of the first online classes I ever took was a statistics class back in 2002. As a computer programmer I use different algorithms and formulas for creating passwords for security issues. As an Analyst I compile user data and use that data to understand usage patterns and look for areas where there can be improvements. I still struggle with what I consider are abstract ideas of probability, the calculation of dependent events when there gets to be three or more events still doesn't make a whole lot of sense to me, but I'm getting there.
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