TODO: Piccies (especially later on). Tidy text. Add examples/tests (to every page?)
TODO: The stuff at the start needs putting into one page or another.
TODO: Explain notation (in sidebars? In comic balloons?) for things like P(AnB)
TODO: To keep teachers happy, explain sets and events
TODO: Consider making it hyperlink-happy so that we can crossconnect - you can get the explanation of sets from any point, rather than forcing a particular reading order.
TODO: It doens't matter what you NAME things, you can rotate the names at any time and everything stays the same - but it has to be ALL of a name - you can't rename them only half way through. (Look this up under 'beta reduction' in 'lambda calculus' if you really want to know the why and wherefore of it. Just thinking about it a bit should be enough for now.)
Put this in BEFORE the gygax gameshow.
TODO: Make sure that each section can be read standalone and doesn't rely upon previous terminology (at least, not terminology that involves cats)
TODO: Put this chunk somewhere
Terminology:
P(whatever) is the probability of 'whatever' happening.
Generally, probability is represented by the letter 'p', but if we have more than one, we can use q, r, s etc. If we're using a whole lot - preferably related ones, we can use p1,p2,p3 instead.
When we get the chance, p is the 'before' probability, and 'q' is the 'after'.
Or, sometimes, q is the chance of p NOT happening. q = (1-p). Used that was is just to save space.
Sometimes this is written as !p.
Event are (or should be) in upper case. We will write both P(A) and P(A=a) - although technically the latter should be written as P('big double barred A'=A)
TODO: Give thanks for gygaxian gameshow idea
TODO: Apologies for lack of rigour - disclaimer "This is to inform and inspire, but in a few places it simplifies enough to be painful. Beware the simplification and be prepared to learn corrections later.")
TODO: Work the other two bits into the main narrative. (Examples pages?) Not the foxy bubbles one!
TODO: Note somewhere that people are NOT truly random, and given enough people you've find a pattern of box choosing something like
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/\/ \/\
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TODO: Did I ever introduce the notation P(A=a) means 'the probability that A = a'? If not, do so.
TODO: The use of 'on average' for probability - noting that 72 tries at p=1/6 isn't exactly 12, it's 12 on average. There's alwys a chance that it's 72, and a chance that it's zero.
(And that chance, of getting x out of n at probability p, is nCx * p - it clusters around the average np, but there's a chance right out to the edges)
Expectation, not prediction. The whole 'do it a lot of times' as a sampling of an infinite number of tries.
TODO: Note that we're not looking (yet!) at what happens if the probability changes over time. We're assuming in all of these that if you roll a die once you get the same spread of outcomes the next time. And the time after. And so on.
TODO: With replacement. Without replacement AFTER we've done combinations etc.
TODO: Sock division by way of having the boundaries between basckets as items themselves.