Probability. I had fun; I hope the class did.
Started with the easy definition: (# of successes)/(# of possibilities), for throwing a die. Pointed out the circularity of the definition since the possibilities have to be “equally likely”, and that’s just “probability” by another name. The definition “probability of a 4 is 1/6 because in the long run the fraction of 4’s will be close to 1/6″ will only work if you can be precise about what “in the long run” and “close to” mean. So that’s another dead end (at least for this course).
Examples from decks of cards (probability of a spade, of a face card) turned into a discussion of blackjack, which I won’t try to summarize here. It included a discussion of how to count the number of two card hands (easy for a small deck – just list them – harder for a 52 card deck since you need a method. I told them 52*51/2 and quickly explained why but time was too short). Counting the number of blackjacks is even harder. We didn’t try.
One student asked if the probability of a blackjack depended on where you were sitting at the table. The answer is (as usual), it depends — yes if you know the cards dealt to the players before you, no if you don’t have that information.
That led naturally to card counting, which many wanted to know about. Here are two links I will point the class to: How to Play Blackjack and Blackjack Card Counting – Introductction (the spelling mistake is in the original).
Of course none of this can be on the exam. That doesn’t make it less important. I’m not sorry to have spent the time this way.
I will put some (simplified) card counting problems in as Common Sense exercises.
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