Yikes! Math horror! 
[Jun. 28th, 201507:59 pm]
John

Someone posted this: http://www.museum.state.il.us/muslink/pdfs/re_dice.pdf. And they suggested using it to teach probability. Which... good, but a little advanced.
Here's the idea: you paint 5 sets of plum stones  two are black on one side, natural on the other. The other 3 are white on one side and natural on the other.
If you note that there are four different totals for the whitehalf stones (0, 1, 2, and 3 white sides showing) and three different totals for the blackhalf stones (0, 1 and 2 black sides showing) you can see that there are 12 values.
Here's where the site blows it. "Students should be aware that there are 12 different outcomes possible, the odds are 1 in 12 of any one outcome, and the different odds of scoring 8, 3, 1, and 0 points."
That's a very good statement of a basic principle of probability, and it is 100% completely wrong.
First: there are *32* combinations possible. It's true: a lot of those combinations end up being precisely the same, but that doesn't mean they have the same odds.
For example: 5 natural side stones are 1/32. One white stone showing is 3/32nds  is a 1 in 32 of getting: no black, and only the first white stone white; no black and the second white stone white; and no black, and the third white stone white. In Math, the odds of any combination is C(2,b) x C(3,w), divided by 32, where b = number of black stones, and w = number of white  and C is the "nonordered combination" function.
One black and one white is 6/32  there are two possible stones to be black (or natural, if you're a stonehalfnatural kinda person)  C(2,1) = 2  and three possible stones to be white (C(3,1) = 3).
What bothers me about this most is that this is *just* close enough to correct that it could confuse some teachers who insist that all colored (2 blacks and 3 whites) must occur nearly 3x as often as it actually occurs, and confuse the heck out of some kids who start to notice the statistical drift. 

