We continued talking about probability theory today, covering three topics:
1) Expected values, which is sort of the average outcome you'd expect from an event. This is useful in simplifying a lot of problems. The average of 1d6 is easy to compute directly (add together 1+2+3+4+5+6 and divide by 6), giving 3.5, but the average of 100d6 is not easy to compute that way (since there are 6^100 possible outcomes) but since expected values have certain rules, we know that the expected value of 100d6 is just 100 times the expected value of 1d6, so it's an easy computation.
2) Weighted averages. If you don't have a uniform distribution (meaning different results happen more or less frequently than the other) then figuring out the average takes an extra step - you have to sum together (each of the outcomes times their probabilities).
3) Probability trees, if you have a sequence of events, like coin flips, or dice rolls, and they have different outcomes, you can use a probability tree to work out what the overall expected value is by working from the bottom up.
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